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1. Schaum's Outline of Linear Algebra
2. Linear Algebra
3. Introduction to Linear Algebra,
4. Linear Algebra Done Right
5. Linear Algebra and Its Applications,
6. Linear Algebra For Dummies
7. Linear Algebra and Its Applications
8. Student Solutions Manual for Linear
9. Linear Algebra: A Modern Introduction
10. Linear Algebra Demystified
11. Linear Algebra and its Applications
12. Elementary Linear Algebra
13. Introductory Linear Algebra: An
14. 3,000 Solved Problems in Linear
15. Linear Algebra with Applications
16. Linear Algebra with Applications
17. Linear Algebra
18. Matrix Analysis and Applied Linear
19. Linear Algebra (2nd Edition)
20. Applied Numerical Linear Algebra

1. Schaum's Outline of Linear Algebra Fourth Edition (Schaum's Outline Series)
by Seymour Lipschutz, Marc Lipson
Paperback: 432 Pages (2008-08-26)
list price: US$18.95 -- used & new: US$10.75
(price subject to change: see help)
Asin: 007154352X
Average Customer Review: 4.0 out of 5 stars
Canada | United Kingdom | Germany | France | Japan
Editorial Review

Product Description

Schaum's has Satisfied Students for 50 Years.

Now Schaum's Biggest Sellers are in New Editions!

For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates its 50th birthday with a brand-new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study.

Schaum's Outlines-Problem Solved

More than 500,000 sold!

Linear algebra is a foundation course for students entering mathematics, engineering, and computer science, and the fourth edition includes more problems connected directly with applications to these majors. It is also updated throughout to include new essential appendices in algebraic systems, polynomials, and matrix applications.

... Read more

Customer Reviews (7)

5-0 out of 5 stars To the point, rigorous, inexpensive
I cannot tolerate books that beat round the bush or dumb things down. I value rigor and directness. That's why I love Schaums outline series. I used this book before taking classes in Econometrics, and learnt a lot in very little time, thanks to the direct style of this book. Thanks a lot, Schaums series.

5-0 out of 5 stars It makes linear algebra easier if you are learning it in a class
So, I did not have this book while taking linear algebra, but I now wish I did.You see, I let my girlfriend borrow it for her class, and now, despite the fact that we've broken up since then, she still has the book and tells me it is saving her life.I did look through the book before letting her use it, and it seems to be a great,fairly comprehensive outline of linear algebra (go figure from the title, eh?).You will need a math-ish background to be able to follow the concepts presented, so I recommend this for use in a class or as a reference, but not so much as a "first time" study aide.However with all the worked examples it provides (and a little gumption) you could still learn a lot about linear algebra even without much of a math-background.It will be, almost certainly, much easier to understand than your typical text book.I would put in a word of caution, though, if you are planning to lend it to your girlfriend...

4-0 out of 5 stars Good revision book, quite a few errors
First of all, this book helped me get 97% in my linear algebra test!

Heaps of practice problems, good explanations, but quite a few errors (minor).

Get it if you're struggling with linear algebra.

3-0 out of 5 stars just okay
It's a good study tool when used as a supplement to a class or another textbook. The problems are chosen well, the only problem is the book is riddled with errors. Fortunately, they adequately explain their solutions enough that you can go back and verify that they are the ones making the error. Overall I recommend it for the price.

5-0 out of 5 stars very helpful
I found this book to be very helpful.
Pros: Excellent as a supplement or even as a text. Lots of worked out problems, some are even proofs of theorms.The explanations are to the point and easy to understand.Good for math, physics or engineering undergrad majors.There is enough material for 1.5 undergrad semesters of Linear Algebra. Very appropriate for math GRE subject test review.
Cons: none
This book does not have the abstract algebra style, so not for math graduate school.
... Read more

2. Linear Algebra
by Georgi E. Shilov
Paperback: 387 Pages (1977-06-01)
list price: US$16.95 -- used & new: US$10.00
(price subject to change: see help)
Asin: 048663518X
Average Customer Review: 4.5 out of 5 stars
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Product Description
Determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems; hints and answers.
... Read more

Customer Reviews (21)

5-0 out of 5 stars Excellent text for the mathematically mature
I bought this book about four years ago and haven't got around to writing this until now. One reason is that I still haven't finished the book, although I've gone through the first five and half chapters in detail as well as bits and pieces of the later chapters. I've seen enough to know that this is a first rate text. I majored in math, but even after graduating my linear algebra was pretty weak. This is the perfect book for either a second exposure to the subject or as a refresher after some time away from the subject. It starts from the basics but might not be suitable as a first text (except for the strongest students). Even then I'd recommend simultaneously going through a simpler book to get more concrete, computational experience.

This is definitely a dense book. The first chapter alone covers just about everything you need to know about determinants, although no geometric interpretation is given. It has material that isn't covered in most books, namely the Laplace expansion for the determinant, which is used later on in a clever way to prove Det(AB)=(Det A)(Det B). The order of some topics is slightly unusual (compared to the other books that I've seen), but it leads to nice proofs later. For example, the rank of a matrix is defined as the size of the largest minor with nonzero determinant and then the other definitions are shown to be equivalent later on. In the meantime this definition is used to prove certain theorems about dimension and the size of a basis, and so on. Also, he introduces factor spaces and even the isomorphism theorem V/ker f ~ im f (I need LaTeX).

I do find the later chapters pretty daunting. No doubt this is mostly because I need more time with the material, but looking at Shilov's treatment of projections and least squares problems for example, I could see myself struggling mightily if I hadn't already digested the material in other books. Maybe the perfect route to a second course in linear algebra would be the first 5 chapters of Shilov, then as much of Axler's Linear Algebra Done Right as possible, then back to Shilov, etc. Nothing beats Shilov's early chapters, but there are some later topics in Shilov's book that I think Axler covers better.

There are a few other minor complaints. Obviously there are some typos but I haven't run into anything too major. Maybe a mixed up subscript or if I remember correctly, saying "no more than" instead of "no less than". Also, major theorems aren't really labeled as such or separated in any way from anything else. The rank-nullity theorem is just labeled 4.12b or something like that.

Still, this is a 5 star book all the way, even before you factor in the price. Given that this is about $12, how can you possibly go wrong? Highly recommended.

4-0 out of 5 stars Translator transformed a masterpiece into a monster's piece
5 stars for the author, but regrettably only one star for the translator. Dr. Richard Silverman should stay well within his expertise which is mathematical translation. Please do not second guest the thinking behind the Russian genius. Dr. Silverman, in the process of freely editing, transformed a masterpiece from a mathematical authority into a monster's piece. There are numerous typos and simple algebra, and sometimes conceptual errors to make the book legitimate for learning mathematics. For example, in section 6.1, the lengthy construction of the "Canonical Form of the Matrix of a Nilpotent Operator", The translator completely mixed up the construction of space (H sub r) making it almost impossible to follow. It is not a typo error as claimed by the translator.

However, regarding to the real content of the book.
It is a masterpiece from a mathematical genius. Brilliance mathematical expositions and beautiful proofs. The expositions are coherent and rigorous. And though, it would have been very readable if the mistakes were corrected.

5-0 out of 5 stars Excellent Linear Algebra Text
I needed to refresh my understanding of linear algebra and so I read Shilov.

I studied matrix algebra 40 years ago and I needed to refresh my algebra skills.This text was just exactly the review I needed.

3-0 out of 5 stars Slow going (for me anyway)
Full disclosure: I'm not finished with this book yet.My last encounter with linear algebra was in 1978, so I expected some head-scratching.But it took me many hours just to get 25 pages into this book.Linear algebra is not Einstein science, so I was worried.I compared this book to my 30-year-old college textbook, and the college textbook wins.This book is lacking in examples.A theoremis presented, then proved, then given a reference number, and then pops up later by reference number, forcing use of many bookmarks.

On the positive side, the price is a bargain.And, the translation from the original Russian is absolutely invisible.

5-0 out of 5 stars rigorous and rewarding
Shilov's Linear Algebra is a great book for mathematicians wanting a detailed and rigorous exposition of the subject matter.All the standard topics in linear algebra are covered, such as: determinants, cofactors, minors, and more topics in matrix algebra; linear spaces; linear and bilinear operators and forms; quadratic forms; matrix representation of linear functions; eigenvectors and eigenvalues; Euclidean and Hermitian spaces; orthonormal bases; etc.Some more advanced topics are also touched upon; there are brief sections on tensors, multilinear forms, and spectra, jets and polynomials, but I wouldn't recommend this book to learn about these, as there are more complete treatments elsewhere.There are also two appendices, one on some basic representation theory, the other on category theory.Again, this is not the best book to learn about these topics, but it is interesting that they are included, perhaps to show some theoretical applications of linear algebra.
The proofs are detailed and precise, making the book great for self-study.A few of the proofs are actually quite original, which is impressive for such a well-worked subject.There are also large and comprehensive problem sets at the end of each chapter, with either full solutions or hints given in the back.This book is also good in that it is mostly self-contained, presupposing almost no prior knowledge of linear algebra or other fields of mathematics.
This would probably not be a good book for someone learning linear algebra for the very first time, or for someone looking for a quick-and-easy reference for formulas.Shilov takes the pure mathematician's approach of presenting everything with a high degree of generality, probably more than would be necessary for most undergraduate college classes in linear algebra or for engineers and computer programmers.But if you're a mathematician looking for a complete and self-contained account of this fundamental subject, or just someone who enjoys the rigor and beauty of pure mathematics, this is the book for you. ... Read more

3. Introduction to Linear Algebra, Fourth Edition
by Gilbert Strang
Hardcover: 584 Pages (2009-02-10)
list price: US$87.50 -- used & new: US$75.00
(price subject to change: see help)
Asin: 0980232716
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'.

Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, fourier methods and the FFT, linear programming, and computer graphics.

Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.

Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell. ... Read more

Customer Reviews (46)

1-0 out of 5 stars Not the worst, but close
As an earlier reviewer said, " A wonderful prof, but a terrible, author. "I may have added a couple of more "terribles" had I coined that sentence.As is the tendency with all math majors, massive step skipping in writing texts is the norm, and in fact is seen as a useful tool to get the student to "think" about the concept and prove it themselves.So, since I am likely not as smart as most, when reading the text, I have to "grind it out" and verify every last detail of every equation to be able to "get it".When stepping through the first few chapters of the book and I found the inevitable errors in equations and graphs/figures that are the result of the author not "grinding it out".I assume attention to that level of detail is boring after all of those years as a math major.

It seems the reviewers who think this book is wonderful for non-math majors are math majors!As a post bac student in Computer Science with B.S. in Mechanical Engineering, I needed to review the concepts from long ago in which I was so fundamentally sound to begin with.I was left with, "Is this even the same subject that was so simple the first time around and that we used in nearly every course?".I resorted to digging out my "Vector Mechanics for Engineers" text and reviewing.For me, Strang's book is a waste of money and natural resources.

5-0 out of 5 stars Gold Standard
I used this book as self study.I was drawn to Gilbert Strang because it seemed to be the gold standard for linear algebra and the popularity is deserved.The one thing I would like to add is the effect of the use of symbolic math software.I used Mathematica but Strang has some code for Mathlab in the book.People have views on this subject but I find that Mathematica does the job well enough.The effect on me is that it made me feel a little insecure by not doing it by hand.Because finding eigenvalues, eigenvectors and row reduction is tedious, I gave in to the temptation of just writing the code which any highschool student can do.While the working Mathematica gave me a good coding skills, I can't help but feel I have some loose ends by relying on the computer too much.

At times I think that doing the problems was mental hazing.I wasn't able to do all of them particularly the more difficult ones.The problems are divided into two parts: the first is the regular problems and the few hard ones.I didn't even touch the hard ones.I good feature of the chapters is at the end there are worked examples where you are given a problem and solve it before you look at the solution.

Finally, Strang's lectures are available at opencourseware at MIT.I think they are also at Youtube.I look back at my self study now and regret not taking advantage of it

4-0 out of 5 stars Decent but not fantastic

1.The coverage of the four fundamental spaces is fantastic.The pictures showing their dimension, orthogonality etc is very very good and easy to remember.And the importance of the understanding of this topic can not be over emphasized.Prof Strang did an excellent job here.
2.The on-line lectures are excellent.Well at least for most of them.


The SVD part is not excellent.Prof. Strang agrees that this is the climax of linear algebra.But the presentation of this critical topic is not excellent.The link between the four fundamental spaces and SVD is not so clear.And the related pseudo-inverse is also not so excellent.Unfortunately, the video on SVD also suffers from the same problem.But I would not blame too much on the video.After all, I am not sure if an excellent coverage of SVD can be given within one lecture.But the book should have plenty of space for a good coverage.

For a good SVD coverage, I found the following is good.
1) A good understanding of the four fundamental spaces is very important.Prof. Strang does an excellent job in his book.
2) Some internet articles actually provide good introduction, better than those provided in books
3) An article on-line by Dan Kalman is very comprehensive but not the first thing you should read.
4) Trefethen in his Numerical Linear Algebra has some good (but not complete) description.

4-0 out of 5 stars School Book
Easy to read.

Very informative.

Sometimes would leave you guessing though. Not enough examples.

4-0 out of 5 stars Good Book but with unclear parts (then watch the lectures)
The book is half very good and half with unclear parts. Some topics are explained in a very clear and nice way. Other topics are unclear. One exampleis in page 334 where the author tries to prove that a symmetric matrix always have eigenvalues signs that match the pivot signs. The authors asks the reader to look at the changing of values while they "moves to zero". I still can't see this "move to zero" in the matrix multiplication. In other sections he talks about a topic that is only explained further in the book. One example is in page 310 exercise 31 when the author tasks you to work with the Cayley-Hamilton Theorem, but the theorem is only stated clearly in a following exercise. But I would like to note that things that are not well explained in the book are better explained in his lectures. So if you choose to buy the book I would recommend you to watch the video lectures, which are nice. ... Read more

4. Linear Algebra Done Right
by Sheldon Axler
Paperback: 272 Pages (1997-07-18)
list price: US$44.95 -- used & new: US$22.96
(price subject to change: see help)
Asin: 0387982582
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents--without having defined determinants--a clean proof that every linear operator on a finite- dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus, the text starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.


AMERICAN MATHEMATICAL MONTHLY"The determinant-free proofs are elegant and intuitive."

CHOICE "Every discipline of higher mathematics evinces the profound importance of linear algebra in some way, either for the power derived from its techniques or the inspiration offered by its concepts. Axler demotes determinants (usually quite a central technique in the finite dimensional setting, though marginal in infinite dimensions) to a minor role. To so consistently do without determinants constitutes a tour de forces in the service of simplicity and clarity; these are also well served by the general precision of Axler's prose. Students with a view towards applied mathematics, analysis, or operator theory will be well served. The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library." ZENTRALBLATT MATH "Altogether, the text is a didactic masterpiece." ... Read more

Customer Reviews (54)

2-0 out of 5 stars Very poor quality printing
I have nothing to say about the content of the book itself; it seems to be an excellent book.However, one major problem (that Amazon apparently tries to hide) is that the softcover edition is a print-on-demand book.This wouldn't really be a problem, if the printing quality was anywhere close to that of a normal book.Unfortunately, it isn't.The entire book looks like it was run through a cheap fax machine.There is noticeable fuzziness and pixelation; it is highly annoying, looks terrible, and makes the book hard to read.I cannot believe Springer would produce something of such low quality.I plan to return this book and get a used hardcover copy.

5-0 out of 5 stars Linear algebra made fun!
OK, I admit that I have never much liked matrices (or determinants). Standard textbooks for undergraduates typically seem to devote 200-250 pages to telling one in an informal and concrete way what a vector is, what a matrix is, what a determinant is and how to do all sorts of highly boring / tedious matrix operations, etc., i.e., there is no real algebra in these so-called linear algebra books until one is pretty much bored to tears.And even when they do introduce some algebra, they deal almost exclusively with the reals (with a tiny nod here and there to complex numbers) and the presentation does not provide a unified coherent picture nor prepare one for more advanced mathematics. So if one wants to learn about the algebra in linear algebra, one needs to look elsewhere and Linear Algebra Done Right not only does it right but also makes it fun.The exposition is generally very clear (this does not mean one does not need to work a bit to understand the material!) and since it sticks to essentials, it moves along at a nice clip.What a breath of fresh air!Despite my lavish praise, I would not recommend this book as one's first or only book on linear algebra.But I recommend this book very highly to anyone who wants to appreciate the beauty of (actual) linear algebra or needs a stepping stone to more advanced books such as Roman's Advanced Linear Algebra (Graduate Texts in Mathematics) or books on linear functional analysis and Hilbert spaces such as Linear Functional Analysis (Springer Undergraduate Mathematics Series), Kreyszig Introductory Functional Analysis with Applications or Introduction to Spectral Theory in Hilbert Space (Dover Books on Mathematics).

1-0 out of 5 stars Linear algebra done right
Hate this book. This is purely designed for graduate students but I am an undergrad. I found nothing relevant in this book and I am sure to dump it as soon as I am done with the class. By this book if you're ready for a headache.

5-0 out of 5 stars GREAT BOOK

5-0 out of 5 stars Great book for Applied Mathematics.
Did I just say that a book that has no examples of how to use a concept in applied situations is great for applied mathematics?

Yes. And I mean it.

I'm currently taking a graduate course in numerical analysis, which is about as applied as you can get. Here's how I read my textbook: I read through a section on say, the QR-algorithm for finding eigenvalues. After a long, brutal period of intense focus, I go"what did that just say?", and then I read it again. I think, "what in the hell's an invariant subspace? What's this weird projection operator doing, what's this . . ."

And then I remember how to make the pain stop: Pick up Sheldon Axler's book, and read the appropriate section in his book. Then go back to numerical analysis, and breeze right through the exposition of the algorithm.

Dr. Axler doesn't claim that his book is for applied mathematicians or engineers. He wants you to understand the structure of linear operators. But guess what? Applied mathematics exploits many-no, all-of the deep concepts relating to the structure of linear operators. So if you want to be a good applied mathematician, someday you're going to have learn linear operator theory. If Maple does all of the math you need for your job, then you won't need to learn linear operator theory. And so don't use this book. But realize that someday, you will hit a wall.

Now onto some specifics of the book:

Some have complained about the lack of use of determinants in this book. Think about a mathematical concept that you use over and over again, that you can use as an analogy to other things and helps you go about your day. For me, I understand these concepts down to the very core. Things I don't understand down to the core, I can't extend to novel situations. And if we can't extend a concept to a novel situation, why learn it? Certainly we can tell Maple to compute it if we really need. For me, the determinant is a conceptual dead end. Not once in my life has anyone been able to explain why det(AB) = det(A)det(B). And I doubt that the person who does know finds that the proof very enlightening. Similarly, why should the determinant have anything to do with how a matrix scales it's eigenvectors? No one knows! Ok, you say, but we do need to know if a matrix is invertible, and so we should teach people that the determinant can tell them that. Fair enough. I'll giveyour students a 100x100 matrix, and then I'll come back next year to find out whether or not it's singular. They'll say, well we got 10^-12. And I'll say, "does that mean all that matrices eigenvalues are 3/4,or one of them is zero and you just got round-off error?" They'll have a blank stare, and then I'll estimate the matrix's condition number in a few seconds and tell them the answer. So for engineers and applied mathematics, the determinant is truly useless. Dr. Axler is correct to scrap it.


Some have complained about the lack of solutions to the problems. This is false. There are many solved problems in this book. They just have the solution immediately after the statement of the problem. I find it baffling that if the author had just moved the proofs to the back of the book, and labeled the theorems "Problem", then this complaint would disappear. This is a math book, not a Charles Dickens novel. You read a Charles Dickens novel, you battle a math book. When you read the word "Theorem" in a math book, you try to prove it yourself. Then, after failing, you read the author's proof. I don't see how this is at all a controversial statement, but if people read math books like math books, then no one would complain about the lack of solved problems. The fact that Dr. Axler has to copyright the solutions (provided this is true, I don't know)is a sad testament to the fact that people don't want to battle math, they want to regurgitate it. They would rather sleuth the internet for 12 hours trying to find posted solutions rather than spend one hour thinking. I've done it myself. But once these solutions are available, and people know that sleuthing will prevent thinking, then your book has shot its wad.

This bookhas saved me countless hours. If I value my time at $10 per hour, then this book has already saved me well over $1000. The fact that it is only $30 is a steal. ... Read more

5. Linear Algebra and Its Applications, 3rd Updated Edition (Book & CD-ROM)
by David C. Lay
Hardcover: 576 Pages (2005-09-01)
list price: US$141.33 -- used & new: US$56.00
(price subject to change: see help)
Asin: 0321287134
Average Customer Review: 3.5 out of 5 stars
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Editorial Review

Product Description

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

... Read more

Customer Reviews (37)

5-0 out of 5 stars Linear Algebra.
Linear Algebra by David C. Lay is a great book.It is very thorough at explain the matrix and different ideas in Linear Algebra.
Had no issues understanding the material and greatly helped me in class.I basically could only rely on the book as the professor wasn't as available as he should have.

I basically taught myself Linear with only minor issues that were resolved through practice.

2-0 out of 5 stars NOT A GREAT BOOK
I got this book because I'm taking linear algebra and it is a required textbook. The book does not explain the material clear, and some of the true or false exercises are very ambiguous, it is not base on the general concepts of linear algebra. for example, true or false: A linear transformation is a special type of function, the superposition principle is a physical description of a linear transformation, etc. if you want to learn the basic theory of linear algebra, choose other books.

5-0 out of 5 stars FIRSTCLASSBOOKS:Linear Algebra and Its Applications
Originally, I gave bad feedback, but after speaking with the company (First Class Books), they went out of their way to rush my textbook at a great price for a new book. I reccomend them.

1-0 out of 5 stars Apparently not a self-study book
For those of you who plan to find a self-study material, do not count on this book. I'm a PhD in computer science department and I'm looking for some books to brush my understanding about the linear algebra. I'm looking for "notions" instead of "derivations". The author does a good job in the first few chapters but I quickly lost after the vector space. I believe that I have some background, though not solid, in linear algebra, but the writing is so dry that I cannot easily follow the flow. I do believe that the author is very knowledgeable.However, as a self-study material, it would be too tough in my opinion.

If you are looking for a self-study book that is easy to follow (especially for deep topics). Be prepare that understanding the intuition behind the formula is not well addressed in this book. I won't say it's a 1 star book in the view points of quality. But apparently, you learn nothing if you cannot follow it, right?

1-0 out of 5 stars Do Not Purchase From This Seller!
I purchased a book for school from this seller on 8/06 and still have not received it (now 9/06). I tried to contact the seller a week and a half ago and still have not received a response. I would highly advise that you Do Not purchase anything from this seller. ... Read more

6. Linear Algebra For Dummies
by Mary Jane Sterling
Paperback: 384 Pages (2009-07-07)
list price: US$19.99 -- used & new: US$10.89
(price subject to change: see help)
Asin: 0470430907
Average Customer Review: 4.0 out of 5 stars
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Product Description

Your hands-on guide to real-world applications of linear algebra

Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction.

  • Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices
  • Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems

  • Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule

  • Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action

  • Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices

Open the book and find:

  • Theoretical and practical ways of solving linear algebra problems
  • Definitions of terms throughout and in the glossary

  • New ways of looking at operations

  • How linear algebra ties together vectors, matrices, determinants, and linear transformations

  • Ten common mathematical representations of Greek letters

  • Real-world applications of matrices and determinants

... Read more

Customer Reviews (6)

4-0 out of 5 stars not perfect but useful
you might notice a few typos every 20 pages. I can let that go cause I've never been exposed to this subject.

3-0 out of 5 stars The typos are a tremendous shame
I just finished the text. It is a nice easy review. The amount of theory and proofs is kept to a minimum which should please those who are less gifted mathematically. The major issues as stated elsewhere are the number of typos and errors which were not caught in the editing process. Many are obvious and easy to fix. I would encourage the editors of this series to be more careful in the proofing. Perhaps it is too expensive given the low purchase price of the texts. Maybe we should all send in a list of errata and they could print a new edition.

4-0 out of 5 stars be smarter than the book!
I really like the approach of this book, as it uses good analogies, examples, graphs, and figures that appeal to your intuition to give deeper meaning to the subtleties of linear algebra.But it is a shame there are typos and mistakes.One in particular blew my mind - on p. 51 she states " A square matrix is singular if it has a multiplicative inverse; a matrix is non-singular if it does not have a multiplicative inverse."This is exactly opposite of how everyone else defines "singular", but she uses this definition consistently throughout the book, so either it's a mistake or she has decided to rewrite the rules of linear algebra.Either way, it's not helpful!!!

I hate having to make corrections on a book I just paid for, but for the price, what can you expect?Most textbooks on the subject are between two and ten times more expensive, and they have mistakes too.But the other books are dense, dry, and boring.At least this book attempts to make linear algebra interesting, if not fun.

4-0 out of 5 stars useful to me
College was a long time ago - I needed a refresher to do my job; this provided it.

4-0 out of 5 stars Linear Algebra for Dummies
Good explanations, but a disappointing number of substantive typos that make the examples confusing.

I would recommend this book, particularly as a review for those of us who had the subject in college but have forgotten most of it.Just be careful of those typos and keep a pencil handy to make corrections while the details are fresh in your mind. ... Read more

7. Linear Algebra and Its Applications
by Gilbert Strang
Hardcover: 544 Pages (2005-07-19)
list price: US$220.95 -- used & new: US$150.00
(price subject to change: see help)
Asin: 0030105676
Average Customer Review: 3.5 out of 5 stars
Canada | United Kingdom | Germany | France | Japan
Editorial Review

Product Description
Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics. ... Read more

Customer Reviews (73)

5-0 out of 5 stars If you are a beginner, this is the book you must read!!!
I highly recommend this book to beginners. Is it possible there is no lemma, theorem or proof in an EXCELLENT math book? Yes! This book presents a very clear picture of linear algebra in a friendly way instead of simply listing some theorems. The words, notations and figures are very appropriate. The author is humorous. Sometimes, I even found I read the book with smile. Unbelievable! If you were scared by math once, you may try this book to retrieve your confidence and enthusiasm on math. It is really quite enjoying reading this book.

5-0 out of 5 stars The best book for a first course in applied linear algebra
As someone who works in an R&D environment (and is called upon to use linear algebra to solve real world
engineering problems), I wanted to put this book in perspective for those who may be unsure of the true value of this book given the variance in the reviews.

1. This book presents an applied treatment of the subject appropriate for a first course. The goal of the
book is to provide the reader with an intuitive understanding of the material. Geometrical arguments and diagrams
are used throughout without apology. Coordinates and matrices are emphasized. Formal proofs are not emphasized.

2. This book is geared toward those doing computations in the real world.Linear algebra
is the workhorse of modern applied mathematics. Any modern course on linear algebra that does not cover LU, QR, SVD,
and least squares is out of touch with reality and in my opinion doing a disservice to those who are paying $$$
for an education.Specifically, those who are ever planning
to get a job in engineering or the mathematical sciences will at some time be expected to solve (or understand how
software like MATLAB solves) least squares problems, systems
of linear equations, eigenvalue problems, linear ODE's, optimization problems, etc...As a result, this book
is focused on matrices and computations.This book is practical in the sense that in the real world -where
numerical solutions are usually required - we are
forced to deal with a basis-dependent
finite-dimensional representation of our problem.

3. Those who require a second course in Linear Algebra covering Jordan Forms, the theory of linear operators, and more advanced material
will not have to unlearn anything from this book.In fact this book is a good stepping stone to further study.
For example, someone who comes to Hoffman/Kunze or Halmos after this book will better appreciate the more
abstract approach based on linear transformations. After all, how can anyone understand or appreciate
a formal abstract treatment of this material before one has a firm grasp of what is being abstracted?

4. Strang has a webpage with video lectures that augment the text and shed additional insight on the material. These
lectures are excellent and really demonstrate the love Strang has for teaching this subject to others.
In my opinion he has done the scientific and engineering communities a big service by writing this book and posting his
video lectures.

5. Strang has another text on Linear Algebra, Intro to Linear Algebra. Although that text is geared at slightly
a lower level, I like the present text better as a learning tool.
The Intro text is slightly more disjoint in its presentation
and seems to leave more for the reader to discover rather than just presenting the information.

6. If you really do not like Strang's writing style (which is very conversational, and in my opinion, better
than the dry style of other texts), tryMeyer's treatment ("Matrix Analysis and Applied Linear Algebra").Meyer is more of a traditional text and provides
material for both a first and second course on applied linear algebra (with more emphasis on a second course).

Good luck.

5-0 out of 5 stars Wow...more than I ever wanted to know!
This book takes on the very difficult challenge of linear algebra. The book is pretty good, but acces to Strang's online lectures is awesome! This guy is a very good instructor, and I highly recommend watching his lectures when going through this book.

5-0 out of 5 stars Still the clearest text on Linear Algebra
I was fortunate to have taken this course and Applied Mathematics from Gilbert Strang at MIT in the mid-late 1980's. We used this and his Introduction to Applied Mathematics texts. The revised edition of this text is updated and contains newer applications, and is current for today's students.

The texts (both of them) were the clearest and most relevant texts in mathematics that I ever used. This, coupled with Professor Strang's enthusiasm and down-to-earth teaching style made these courses actually enjoyable to this geology major. I use both texts as references to this day in the increasingly numerical science of geology and geochemistry. Coupled with Matlab, the texts are very helpful in leading me through development of numerical models in my research and teaching.

5-0 out of 5 stars A Review of the 2nd Edition
"Linear Algebra and Its Applications" by Gilbert Strang is currently in its 4th edition, but this review is of the 2nd edition.I haven't seen the 4th, but I assume that it is as good as (if not better than) the 2nd.

The text is an excellent introduction to the subject.I was a new graduate student in applied mathematics in 1980 when I took a two-quarter sequence in linear algebra using this textbook.There are many other textbooks on the subject, virtually all of them in the traditional "Theorem-Proof with examples" format.It's easy to follow the logical flow in those texts, and that can sometimes be reassuring.However, Strang's textbook gives the reader deeper insights into the subject, though the reader will sometimes have to work harder to harvest them.It can sometimes be maddening to follow the logical flow in Strang, to separate the theorems from examples from observations.But the struggle is well worth it.I never found any logical flaws in Strang's reasoning (the same cannot be said for other texts), and Strang's notation was always conveniently general without being awkward.Over the years I have referred to Strang on minor points when other texts left me confused.

In short, I would recommend this book to any student as a reference, for self-study, or as a course textbook.But be ready to do the work to get the best possible understanding from it. ... Read more

8. Student Solutions Manual for Linear Algebra with Applications
by Otto Bretscher
 Paperback: 184 Pages (2009-03-02)
list price: US$36.67 -- used & new: US$33.00
(price subject to change: see help)
Asin: 0136009271
Average Customer Review: 2.5 out of 5 stars
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Editorial Review

Product Description
This manual contains completely worked-out solutions for all the odd-numbered exercises in the text. ... Read more

Customer Reviews (60)

1-0 out of 5 stars Poor textbook.Would have given 0 stars if possible.
Do not buy this book unless it is absolutely required for your class.The other reviewers discussing the lack of clarity and completeness in this book are telling you the truth.The presentation of the information is poor.

It's not that people are giving it bad reviews because it isn't "Mathematical" enough.Textbooks do exist that give a good treatment of the subject without going into gory detail.However, this book has information haphazardly organized and essentially glosses over almost everything in a "you get the hang of it, right? Lets move on" type feeling.

Find something else to buy.

4-0 out of 5 stars Linear Algebra Book
The book was received quickly for a good price.Explanations in the book aren't very clear though.

1-0 out of 5 stars waste of money
This book was required for my Linear Alg class last semester. Like everybody else, I'm going to add another one star for this poor written book. I have about three other Linear Algebra books and this one has the most illogical order. It teaches linear transformation without even saying what a vector really is. It teaches you matrix multiplication after linear transformation. It never says anything about the dot product. So I think that the author assumes you to know something in advance. At some point you will go to a dead end. You'll found that the explanation is not enough. So you'll end up looking for other books or some other sources to help you understand the material. That's what happened to me. Fortunately, as I looked for helps on the net I found a youtube channel with awesome video tutorials.It is KhanAcademy. The guy is so famous that he's featured on TV news. He's a hundred time better than my professor.

So, my advice is NEVER buy this book. Spend money for something else. If you want an easy A and a clear understanding of basic Linear Algebra, check out that youtube channel: KhanAcademy.

5-0 out of 5 stars Best textbook I've taught out of
Bretscher's linear algebra book is the best textbook I've taught out of, from 4 years of college teaching. It is thoroughly well written, in considered and elegant prose. The three huge advantages of this book are, firstly, it provides motivation, both scientific and historical, for all the concepts introduced. Secondly, the organization is very well thought out and can be made to flow nicely (despite, or perhaps because of, not being canonical as other reviewers complain about). Thirdly, computational and conceptual issues are introduced alongside each other, so that one understands the practical relation between the Gram-Schmidt algorithm and QR-factorization, for example. The dynamical systems material is very nice, as is the explanation of least-squares minimization. There are plenty of exercises from the trivial to the conceptual, although sometimes i would have preferred more exercises of middling difficulty. The book starts with systems of linear equations and introduces abstractions gradually, intended as a transitional course for would-be mathematics majors. For my student body of mostly economists and mixed scientists, the march of abstraction started to become hard, and adding more problems of the down-to-earth variety in later chapters might help.

In summary, I would recommend anyone considering taking or teaching a course in linear algebra to look over this book. Other books (Strang, or Schaum's outline for extra exercises) might be handy for different levels of students, but this is a fine book and worth leafing through for the historical notes and overview of the subject alone.

To the reviewer who complained the book introduced subspaces before spaces: I find the book's choice on this and similar matters very sensible. Every finite-dimensional space is isomorphic to R^n, and that's the setting where linear algebra first becomes useful, and where subspaces arise naturally as kernels and images. Later one notices that the same ideas apply in more general settings - but why leap into the void of generality before the most comprehensible examples are understood? Examples first!See Tim Gowers' comments on the subject in his blog.

1-0 out of 5 stars Worst Piece of **** I ever read in my life.
I am going to skip the intro and get on with the problems of this Son of a ***** textbook.

1. This has got to be the hardest math textbook I have ever read in my life. And I don't mean in a challenging way, I mean in a difficult to understand way. They do an extremely poor job on explaining Linear Algebra, examples are hard to follow, and there is no fundamentals at all. On the top of that, I think I've actually gotten dumber reading this pile of **** because I had to Google information, just because I was stuck on homework. This books believes that if they only show the theorems, definitions and a few USELESS examples, the student will learn. So to sum this all up, you won't learn any fundamentals or any tricks on how to solve matrix operations. Sometimes the author gets ****ing lazy and decided to let you do the proofs as homework problems. And no, these aren't proofs where you prove "if this, that happens," these are proof of definitions and properties, and this happens almost every chapter.

2. I want to talk about the "examples" more because they are worth mentioning. The book doesn't provide you with a solid example, even if it did, there wasn't enough to fully understand the concept. For instance, in Chapter 2.1 Ex5, it tells you about rotating a vector counterclockwise but the example doesn't tell you how to rotate clockwise. So on any problem that asks you to rotate clockwise (problem 34), you are screwed unless you read ahead into Chapter 2.2. And this happens all the time. In Chapter 3.4 they tell you how to do a transformation with coordinates in subspace, but the only example they provide you is orthogonal projection. None of the assign problems had to do with orthogonal projections, so again you are screwed unless you read ahead or asked someone for help. The only way to get around this is when your teacher assign even problems, and you do the odd problems just to check on the solution to see if it matches. That is literally the only way you will learn.

3. The solutions..... This is where the textbook bites you in the ass, and gets credit dock off your homework. The solutions in this textbook are so inconsistent, it is meant to confuse students. In Chapter 3.1, the solution to a Kernel of a transformation is for example [1, 0, -1]. Then, in Chapter 3.2, the textbook changes its ****ing mind and decides to write the same kernel of the same transformation as [-1, 0, 1]. Technically they are the same kernel, but that isn't what the solution on the back says, or the solution manual. So you can probably guess what's going to happen when the pathetic TA grades your homework. I am not kidding, everyone in our class had points taken off their homework because the kernel solution didn't match the solution in the manual, even though they are the same exact thing. We never knew what we did wrong until a few weeks after. So by reading from this textbook, you won't learn from your mistakes, you are going to keep making mistakes and suffer with it for the rest of your life!

4. Another thing I want to touch upon is the **** solutions the textbooks provide. The solutions are inconsistent, confusion and most of the time useless. Sometimes the questions are a bit complex, and if you look on the back in the solutions, they graciously said "Answers to more theoretical questions are omitted." (this includes graphs). Good job! at the same time, the textbook might as well tell every college student to go **** themselves! Sometimes the solutions doesn't even match the questions being asked. For instance Chapter 4.3 asked you write the basis of kernel, image, and the rank. On the back, each solution only has one answer, sometimes its a kernel, sometimes it is only the image, other times it's the matrix put into RREF. So unless you know how to do it and you gotten the problem right, the solutions won't help at all.

5. This last part consist the many ways how irritating the book can be. The books recycles a lot of the theorems and definitions. In Chapter 4.1, the examples are just a re-use of definitions and theorems from the previous chapters. Another things is that, some problems in the end are so tedious they tell you "You may use technology" (matlab?). Other times, the problems are too simple. Last but not least, some of the examples are written so it confuses you. Instead of a decent step-by-step answer, you get a cluttering of matrices and everything looks like a complete mess.

So let's recap:

1. Just a useless cluster of definition, theorems, and examples
2. Useless examples that don't help with the homework at all
3. Asking you to do proves as homework
4. Inconsistent Solutions
5. Inconsistent Solutions in the solutions manual
6. Lack of helpful solutions (no graphs)
7. Reusing the same theorems and definitions
8. Inconsistency in problem's difficulty
9. And a ton of other things!...

I can seriously go on and on about this pile of **** but it is starting to make my head hurt. This book isn't just bad, it is ****ing horrible. You don't learn anything, and what is worst, the book struggles you if you actually wanted to learn. If you designed a machine that turns things to opposite (black to white, big to small), you know what you will get by putting this book through that machine? The Holy Bible! This text book is a joke, the author clearly doesn't care if the students learn and he just wanted an easy cash-in. Unless you seriously have to take a class that requires this ****, only get this textbook used. I can't believe I have to put up with this textbook for another quarter.

... Read more

9. Linear Algebra: A Modern Introduction
by David Poole
Hardcover: 768 Pages (2010-05-25)
list price: US$207.95 -- used & new: US$144.99
(price subject to change: see help)
Asin: 0538735457
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
David Poole's innovative book prepares students to make the transition from the computational aspects of the course to the theoretical by emphasizing vectors and geometric intuition from the start. Designed for a one- or two-semester introductory course and written in simple, "mathematical English" the book presents interesting examples before abstraction. This immediately follows up theoretical discussion with further examples and a variety of applications drawn from a number of disciplines, which reinforces the practical utility of the math, and helps students from a variety of backgrounds and learning styles stay connected to the concepts they are learning. Poole's approach helps students succeed in this course by learning vectors and vector geometry first in order to visualize and understand the meaning of the calculations that they will encounter and develop mathematical maturity for thinking abstractly. ... Read more

Customer Reviews (23)

5-0 out of 5 stars Bargain
I purchased this book for my linear algebra class.I was able to get it much cheaper then the college bookstore was selling it for.

I did not buy the answer key because I found it not worth the price people were asking for it.Unfortunately this may lead to frustration, but usually the professor will go over the hard questions in class if there is time.

The book is not overly complicated as long as you understand what you are reading.You may have to reread some things for understanding, but overall it is an easy read (at least it was for me).

I do believe that there is now a 3rd edition.

5-0 out of 5 stars Exactly what I needed
Bought this book for a college class. It was the right one and a bit cheaper than the bookstore.

4-0 out of 5 stars A Good Linear Algebra Reference
Having been away from academics for a while, I thought I could use a bit of a referesher in some of the basics. Having learned Linear Algebra using Hugh Campbell's text, I was in for quite a surprise when I began using both Poole's and Lay's texts as refreshers. Both treat the theory of matrices the same. However, Poole introduces the notions of vector spaces early on with clear explanations. The one failing of this text is the treatment of determinants as an afterthought. Rather than have its own chapter, as in Lay, this is a subsection treated more as a curiosity. The development and power of determinants is downplayed all around, but especially in Poole. Overall, however, it is a very good beginners text on a very powerful math subject.

1-0 out of 5 stars Numerous errors
Besides copious amounts of unnecessary jargon and run-on sentences, the listed solutions (both in the appendix and separate [$$$] solutions manual) for problems in this book are frequently incorrect.BIG INCONVENIENCE AND WHOLLY UNACCEPTABLE; given that few problems in linear algebra are quickly processed by hand.If you use this text, expect to spend an hour on one problem attempting to find errors in your approach when in fact there are none, and the listed solution was just wrong.

Instructors and students agree that the frequency of incorrect answers is the biggest problem with this text.

Thou art warned.

5-0 out of 5 stars Can compensate for a bad instructor!
Having read a couple of books on the subject, I really think this is an ideal choice for any introductory Linear Algebra course. Poole's emphasis is clearly on readability for a range of students and building intuitive understanding on a vector-based foundation (where other texts have you lose sight of this through endless computations and sets of matrices). He provides intermittent examples of appropriately rigorous proofs without inundating you (lets you fill in the details in a few exercises) and always offers techniques to help you practically approach types of problems. I'm not a hardcore mathematics person - mostly taking these courses to fill my requirements for teaching high school physics - but I can honestly say that you can carefully read through a section once, and blaze through many problems that are on par with most other texts' (Poole, thankfully, is very generous with # of medium-level practice exercises, and carefully selects challenge problems that are enlightening but still in the scope of the book!). Just as a heads-up, this book doesn't always use the "classical" LA terminology (example: Chapter 5 doesn't emphasize that it is actually dealing with "the Fundamental Theorem of Linear Algebra"). However, it doesn't skimp on any vital intuitive/conceptual implications these theorems bring to light...

Ultimately, this book retains value even after you finish the course (keeping it, when I have the time to go through the entertaining professional applications of LA the author shows in detail). I would seriously consider buying books by this man if he published on other subjects, even if I didn't necessarily need the course! ... Read more

10. Linear Algebra Demystified
by David McMahon
Paperback: 255 Pages (2005-10-28)
list price: US$19.95 -- used & new: US$11.64
(price subject to change: see help)
Asin: 0071465790
Average Customer Review: 3.0 out of 5 stars
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Editorial Review

Product Description
Taught at junior level math courses at every university, Linear Algebra is essential for students in almost every technical and analytic discipline. ... Read more

Customer Reviews (23)

1-0 out of 5 stars Carelessly written
I tried using this book as a review, but stopped reading after a few dozen pages. Almost immediately, you start running into major, non-obvious typos, so downloading the errata is essential. On top of that, many of the examples used to illustrate even simple concepts were unnecessarily complicated and poorly explained. I don't recommend this book.

1-0 out of 5 stars Too many typos and math errors to be of any use
Although the author may know his stuff, it's too bad that McGraw-Hill didn't have an editor review his work or at least have a couple of math majors read through his book and provide him with feedback before they rushed to get it published.

For example, on PAGE 5, the author states that the coefficient matrix is the element at row i, column j (Fig 1-2). As a beginning student, I stared at that for a few minutes before giving up on what the author was trying to communicate. It was only when I turned to PAGE 6 did I see the matrix that he stated was on PAGE 5.

A similar error appeared on PAGE 8 when the author breaks up the discussion on PIVOTS with Figure 1-3 which is a discussion of the upper and lower triangular matrices. But then he continues the PIVOTS discussion on PAGE 9 ane NEVER refers to the Figure 1-3 (because it was actually part of the previous section)!

The next error pops up on PAGE 13 when the number 13 in the sample matrix mysteriously turns into the number 19. And this error is carried through the next page (14). At this point I gave up on the book with it errors and inconsistencies. Luckily, I hadborrowed it from the library.

The only reason I gave this book ONE STAR is because Amazon would not let me give it ZERO STARS.

However, the library also had copies of Schaum's Outline to Linear Algebra and 3,000 Solved Problems in Linear Algebra. These two books were very good and worth buying.

1-0 out of 5 stars The number of errors makes it nearly useless at best, confusing at worst.
It's true. It is full of mistakes. I quit after the first chapter in frustration over the errors. McGraw Hill does not offer an errata for the book. Shame on you McGraw Hill. Either quit selling it, or give us a comprehensive errata so we may fix our already purchased copies. I will be very slow to trust all future books by this publishing company.

1-0 out of 5 stars Even the errata list has errors!
As other reviewers have stated, this book is a great idea, however the execution is just pathetic. The first worked out examples have ADDITION and SUBTRACTION errors! Literally every other example is wrong and the errata only lists about two thirds of the errors.
Avoid this book.

1-0 out of 5 stars What a terrible book . . .
. . . just terrible. I agree with the reviewer that praised the idea behind the book and also with one of the author's stated goals--to provide a quick review for graduate students about to take a more advanced course in linear algebra--but the execution is awful.
This book is replete with errors!Listing them from least to most serious, I found 1)spelling, grammatical and typographical errors2) MANY computational errors (approximately half of the problems have them)3) imprecise usage of vocabulary (in a very vocabulary-driven branch of mathematics)4) SERIOUS errors in definitions and descriptions of procedures (the exposition of one of the most famous algorithms in mathematics, Cramer's Rule (p. 64), IS WRONG!).Also, the few proofs given are worthless except as examples of begging the question, the book in general is poorly written, and--as one reviewer wrote--the answers to the quizzes are incomplete or not given, period.
I am a long-time Amazon customer who orders quite regularly, but this is the first time ever that I have been prompted to write a review.That's how bad this book is. I'm very disappointed; I planned a quick review of linear algebra this summer and do not have time for a textbook-type treatment of the material.
NOTE:I would have given this book zero stars but, as I attempted to publish my review, I discovered that I needed to give it at least one star.It doesn't deserve it.
Shame on the author, the proofreader/editor and publisher.My sympathy goes to those who are just learning linear algebra and perhaps using this book in conjunction with an assigned text; I think they're going to be very confused.

... Read more

11. Linear Algebra and its Applications (Instructor's Edition) Update
by David C. Lay
 Hardcover: Pages (2006)
-- used & new: US$100.00
(price subject to change: see help)
Asin: 0321280636
Average Customer Review: 3.5 out of 5 stars
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Product Description
Publisher: Pearson Addison WesleyEdition: Third ... Read more

Customer Reviews (48)

4-0 out of 5 stars Solid Introduction
This book is a good introduction to linear algebra. The concepts and theorems are really well explained. I would say this would be a really good book to teach yourself, especially if you get the solutions manual.

5-0 out of 5 stars Great way to save cash
Chances are you are a university student in need of a linear algebra textbook. Great news! This older version is exactly the same as the newer version in every which way. If the new edition is a required text for your class this older edition will save you some cash. I bought this edition from amazon.com for 13 dollars. The university bookstore was charging 178 dollars for basically the same book.

4-0 out of 5 stars Good introductory text but may not be enough for the math savvy ...
Happens to read through a few chapters of this book recently.I think it's probably a decent text for someone that has never had Linear Algebra before, but I would recommend Axler's 'Linear algebra Done Right' or Halmos' 'Finite-Dimensional Vector Spaces' for more math savvy students.

3-0 out of 5 stars slow shipping but good product
Product was exactly what I expected. The only thing I did not like was that the shipping took too long.

4-0 out of 5 stars good first introduction
This book is good for a basic introduction, that is for people who have never really seen much linear algebra and who haven't taken a proof-based course before. I used it in my first linear algebra course as an undergrad, and also when I taught an introductory course over the summer.

I especially like that it has some options, such as details of R^n being presented at the end of chapter two as an alternative to covering those facts in the more general context of "vector spaces" in chapter 4. It is not especially rigorous as far as proving things, and does not get too in depth as far as computations though there are some good sections on dynamical systems. So if you are teaching a class that is half engineers and half math majors, it strikes a decent balance.

For anyone who uses linear algebra, you will not be able to get away with having this as your only book, try Strang or Axler for more computational or theoretical (respectively) treatments. It is definitely a good intro though, it gives a decent overview of the main ideas. ... Read more

12. Elementary Linear Algebra
by Ron Larson, David C. Falvo
Hardcover: 560 Pages (2008-07-03)
list price: US$199.95 -- used & new: US$109.99
(price subject to change: see help)
Asin: 0618783768
Average Customer Review: 4.5 out of 5 stars
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Product Description
The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding technology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice. ... Read more

Customer Reviews (10)

3-0 out of 5 stars Maybe my expectations are too high
Typical chapter in this book:

Throw out some definitions and theorems, offer a half-complete proof for a theorem, do some example problems, do some more example problems based on previous examples, give mindless calculator-type end-of-chapter problems.

I'm sure it serves fine as a reference, but it doesn't really bother with trying to be anything more. It is a decent book to learn from, but doing their problems won't really give you intuition into what's going on (even the proofs at the end of their chapters are very basic).

4-0 out of 5 stars very good
The book was in very good quality, better than I expected. It also arrived in due time.

5-0 out of 5 stars I love it
The book was as described, and I received it on time.That was great!

5-0 out of 5 stars Excellent book to learn Linear Algebra
Very often math books can be hard to read or follow.This book is very readable and the examples are well written and explained.I liked the layout of the book and how the authors either reviewed the material or referred to its location earlier in the book.There are a lot of questions, which are laid out in a progressive manner from the basics to the mastery level.The authors also provided resources to assist with the use of technology (though not for the n-Spire yet).Finally, as one who generally needs to see (i.e. classroom) to learn, I believe that with this text I could have taught my self Linear Algebra fairly easily.

5-0 out of 5 stars Very good, solid textbook
I'm taking Linear Algebra right now, and have long since left the lectures behind. The book pulls you along with exciting, unifying concepts for its whole length. And since that's exactly what I've done, I can say that this book is perfect for people who want to study the subject on their own without taking a class; it is comprehensive and clear, covering all of its material on its own without relying on a prof to interpret.

And although linear algebra is probably the most pure math a student just coming off the Calculus 1/2/3 track has seen, the book is loaded with real-world applications. In fact, every chapter ends with an entire section of nothing but applications!

Larson relies heavily on proofs to support and also teach concepts. The important theorems are all proven very clearly. Larson seems to keep in mind that his readers are there because they're still learning the subject matter- something most math books forget when proving theorems for nothing but rigor's sake. There are a few exercises in each section called "guided proofs" which require you to prove some interesting consequence of the section's material and outline basic steps for you to take. These exercises are really a brilliant device for helping students to really think instead of following step-by-step formulas. I would complain, however, that there are many un-guided proof exercises that are difficult and aren't realistic to expect elementary linear algebra students to complete.

Still, reading this textbook is a real pleasure. It's concise and powerful and, importantly, always illustrates all concepts with examples, in addition to the half-dozen-to-dozen general examples for each section. ... Read more

13. Introductory Linear Algebra: An Applied First Course (8th Edition)
by Bernard Kolman, David R. Hill
Hardcover: 768 Pages (2004-08-12)
list price: US$141.33 -- used & new: US$90.00
(price subject to change: see help)
Asin: 0131437402
Average Customer Review: 3.5 out of 5 stars
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This book presents an introduction to linear algebra and to some of its significant applications. It covers the essentials of linear algebra (including Eigenvalues and Eigenvectors) and shows how the computer is used for applications. Emphasizing the computational and geometrical aspects of the subject, this popular book covers the following topics comprehensively but not exhaustively: linear equations and matrices and their applications; determinants; vectors and linear transformations; real vector spaces; eigenvalues, eigenvectors, and diagonalization; linear programming; and MATLAB for linear algebra. Its useful and comprehensive appendices make this an excellent desk reference for anyone involved in mathematics and computer applications.

... Read more

Customer Reviews (5)

5-0 out of 5 stars Like Every Other Review
The book I ordered was expected sooner than I got it; however, seller sent word immediately of the book's shipment and I believe it wasn't his fault for the delay. Seller was prompt and apologized appropriatelyfor the item's slow shipment.

Would recommend to others.

2-0 out of 5 stars Unhelpful in the extreme
Chapters 1, 2, and 4 are pretty well done up to a point.The explanations, examples, and problems are well written and can be followed without cross referencing other texts and pages on the web.You will learn the basics here without too much of a fuss.

Unfortunately, the book has a nasty habit of circular proofs.The author leaves out vital parts of the explanation in the text, referencing other parts of the text, which reference other parts of the text, and then ask you to solve the underlying proof yourself without explaining the fundamentals at all.The book also references FORWARD into chapters you have not gotten to yet in order to solve current proofs.This is not at all helpful.If your professor requires you to solve any of the proofs in any section you will be lost.Good luck.

Chapter 6 is an all-around disaster.Unless you have seen the material before, you will not get it here.The explanation at the beginning of the chapter cannot really be called an explanation.It is more of an obfuscation.The notation is not explained, it is assumed you know it or can figure it out on your own.The proofs in this chapter are a maze of unexplained concepts and hidden information.

Chapters 8 and 10 are more like the first chapters in usability, but the proofs are just as jumbled.

Intervening chapters from the ones I have described are applications of the material from previous chapters and are optional.

Buy another book (or two or three) as a supplement.You will need it.

1-0 out of 5 stars One of the WORST textbooks I ever used
This book sucks at explaining, half the examples in this book just refer you to other examples/exercises that you have to complete yourself. HOW DOES THIS HELP IF YOU HAVE TO DO THE PROBLEM YOURSELF??!? Half the practice problems are theoretical questions that do not help you in understanding the concept whatsoever. The only thing it does is confuse and frustrate you more. Whoever uses this textbook to teach is obviously incompetent and/or has not looked it over at all.

4-0 out of 5 stars A math book
This isn't the easiest linear text I've scene.This also isn't the hardest.The book has a ton of applications, which is good if you're an applied math, engineering, or science major.If your interests are in pure math the applications are still a nice little side note.The book's explanations are explained as clearly as possible without giving up any rigor.At first I didn't like the book, but after looking at several other linear textbooks I realized that these authors did a good job of explaining a difficult topic.

5-0 out of 5 stars Best math book I've ever had
This book is a fabulous resource... explains things in as clear a way as Linear Algebra can be.If you want deeper understanding, many concepts are described in more depth, and most proofs are given in detail.It's notfilled with cartoons and useless pictures like some textbooks, but clear,concise explanations of what turns out to be an interesting and fairlysimple area of mathematics. ... Read more

14. 3,000 Solved Problems in Linear Algebra
by Seymour Lipschutz
Paperback: 750 Pages (1989-01-01)
list price: US$24.95 -- used & new: US$14.20
(price subject to change: see help)
Asin: 0070380236
Average Customer Review: 3.5 out of 5 stars
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Solved Problem Series

These books help readers review and master what they've learned by showing them how to solve thousands of relevant problems. Perfect for preparing for graduate or professional exams, these detailed reminders of problem-solving techniques show readers the best strategies for answering even the toughest questions, including the types that appear on typical tests. ... Read more

Customer Reviews (9)

3-0 out of 5 stars Where's the index?
The cover of this book boldly states: "Great index helps you quickly locate the type of problem you need to solve." Ha! There is no index in the book. This severely limits its utility as a quick look-up for problem solving techniques. The Table of Contents is more detailed than most but it is no substitute for an index.

1-0 out of 5 stars Awful
Just an awful book. It does not cover anything that is in my Linear Algebra text book. It is hard to navigate and some examples refer to diagrams that are apparently in some other book. Stick to something else rather than waste your money on this.

3-0 out of 5 stars 3000 Solved Problems in Linear Algebra
This book has no has no appendix whatsoever to help you find things.Bummer... .

5-0 out of 5 stars Linear Algebra Review
It is good to have this book as a reference in my library.

4-0 out of 5 stars Very good book, worth the price
I got an A in my Linear Algebra class.Part of it may be due to the countless hours upon hours that I studied every week.However, the tools at my disposal helped make the quality of the time worthy.This book is another valueable tool to keep in your toolchest and I'd recommend this as an accompanyment to your class.They do a great job with Vector spaces and Determinants as well as Gaussian elimination.I particularly liked some of the "trick" questions that they stuck in from chapter to chapter (great study aid as many teachers like to stick these types of trick questions).My only complaint is that they prefer to calculate the basis of a row space by non-transposition (whereas our teacher (in our course) used the transposition technique) so I could not really go by that section (thus the **** rather than ***** review) but I can't really fault the author as teachers have their preferences as to how they want their students to calculate certain answers.

I recommend this book.Heck, it's only $24 (you can get a used copy for half the price) and I suspect you'll spend "more" time with this book than you will your actual $100+ textbook (I know that I did).

I'd also like to recommend that you hunt down a used copy (or go to your library and see if they have it) of "Elementary Linear Algebra" by Howard Anton.We had to use the Grossman book (along with its confusing examples and below-average way of showing proofs).After getting frustrated with the Grossman book (and only using it to do the homework problems (but not using the book to actually understand the concepts as the book was way-below-par in doing so) as our teacher assigned us numerous problems), I stuck mainly with the Anton book (any edition after (or including) the 4th edition will do) and this book to get me thru the course with an A.

Get this book though.Even if it helps you understand just one topic more clearly then your textbook (and I'm sure it will help you with dozens), it will have paid for itself.You can never practice enough (as Linear algebra will take alot of your time) and this book will come in handy with their explanation and sample problems (that so many textbooks neglect to show).One word of caution though is that the author prefers to solve some of the problems in ways that your teacher may not.Never-the-less, a good book. ... Read more

15. Linear Algebra with Applications (8th Edition)
by Steve Leon
Hardcover: 552 Pages (2009-09-05)
list price: US$141.33 -- used & new: US$81.69
(price subject to change: see help)
Asin: 0136009298
Average Customer Review: 5.0 out of 5 stars
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Product Description

This thorough and accessible text–from one of the leading figures in the use of technology in linear algebra–gives readers a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. This book stresses the important roles geometry and visualization play in understanding linear algebra.


Matrices and Systems of Equations, Determinants, Vector Spaces, Linear Transformations, Orthogonality, Eigenvalues, Numerical Linear Algebra


For all readers interested in linear algebra. ... Read more

Customer Reviews (1)

5-0 out of 5 stars Great book
I have taught from this textbook (previous edition) and thoroughly enjoyed it. If you are a undergraduate/graduate math major, this is not the book for you. If you are an undergraduate engineering or science major, I doubt you can find a better book on Linear Algebra. What I liked the most about this book is that the author has managed to convey a lot with very few words. For those who want to teach themselves Linear Algebra, this is a great book iff you are willing to figure out missing steps in the theory presented. Trust me, it leads to much better understanding than reading a textbook with all details presented. ... Read more

16. Linear Algebra with Applications (7th Edition)
by Steven J. Leon
Hardcover: 544 Pages (2005-06-16)
list price: US$141.33 -- used & new: US$84.99
(price subject to change: see help)
Asin: 0131857851
Average Customer Review: 2.0 out of 5 stars
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Product Description

This thorough and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra.  The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. Topics such as linear systems theory, matrix theory, and vector space theory are integrated with real world applications to give a clear understanding of the material and the application of the concepts to solve real world problems.  Each chapter contains integrated worked examples and chapter tests.  The book stresses the important role geometry and visualization play in understanding linear algebra. For anyone interested in the application of linear algebra theories to solve real world problems.

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Customer Reviews (8)

3-0 out of 5 stars Math is easy once you know how
Not bad so far.I like how it gets to the point and doesn't overindulge the reader with extra information.

2-0 out of 5 stars Poor examples.
This book is poor at showing examples with complete explanations. They skip too many steps in the process and leave you wondering how they got to the final answer. I don't have experience with other books on this topic, but I would assume that there are better ones out there.

1-0 out of 5 stars Hate this book
Why can't he just include a couple well explained examples for the ideas presented in the book? The sections are short and the very few examples skip multiple steps so I was left wondering how he got from here to there. Text is extremely dry, it's one proof after another and the definition for different ideas isn't clearly illustrated, just written in a bunch of gobbledygook that you have to decrypt like a foreign language. Even my professor admitted he didn't understand where Leon was going with one section and explained it to me in about 2 minutes that made total sense. A big waste of time, seems Leon wants to make everything as vague and hard to understand as possible.

4-0 out of 5 stars Very Satisfied
The book arrived in a timely manner and the condition was just as described. Very satisfied!

2-0 out of 5 stars Linear Algebra Done Wrong
Simply put, this is not the book that should be a bridge to upper-level undergraduate mathematics (ie. algebra and analysis), which is what the purpose of the book is at my university.The author obviously assumes knowledge of basic set theory and proof techniques in the exercises, with no appendix for reference, and most students have not been acquainted with either only having had three elementary computational calculus courses.The proofs of the theorems are rather dull and Leon really fails to give any motivation as to why it might be true.Before my class began, I used it for self-study, and really felt like I could have gotten a better treatment for a different book (which I did later on).The writing in the book is not clear or concise either, I might add.The saving grace of this book is that its exercise section is vast and contains some interesting problems (but the most interesting really require knowledge of how to construct proofs and set theory).It's just really not a great book to prepare anyone for Algebra or Analysis.

For a better treatment, see Brown's Matrices and Vector Spaces. ... Read more

17. Linear Algebra
by Jim Hefferon
Paperback: 450 Pages (2009-06-01)
list price: US$13.95 -- used & new: US$12.55
(price subject to change: see help)
Asin: 0982406215
Average Customer Review: 5.0 out of 5 stars
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Product Description
The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: A semester of calculus. Students with three semesters of calculus can skip a few sections. Applications: Each chapter has three or four discussions of additional topics and applications. These are suitable for independent study or for small group work. What makes it different? The approach is developmental. Although the presentation is focused on covering the requisite material by proving things, it does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class. ... Read more

Customer Reviews (1)

5-0 out of 5 stars One of the best introductory Linear Algebra books I've found
This book is very good -- organization, typesetting and visual presentation, clarity, reasonable rigor (not exaggerated, but not lacking), good examples, several exercises (from simple operational "calculate this" to others that require more thinking or involve modeling) -- overall, it's very good... Hefferon has clearly made a great effort to find relevant examples and to make everything as clear as possible. Lots of theorems are proved, but the book is *not* dense or terse -- on the contrary!

There is also some (just a bit, actually) computer code used as example (Scheme, C, Python, Octave, Fortran).

There are special sections on computer algebra systems, crystallography, voting paradoxes, projective geometry, for example.

Solutions to the exercises are available fro mthe author's website.

Undergrads having problems with Linear Algebra should check out this book.

By the way, the book is also available for free from his website (but the printed copy is absolutely worth the price) ... Read more

18. Matrix Analysis and Applied Linear Algebra Book and Solutions Manual
by Carl D. Meyer
Textbook Binding: 700 Pages (2001-02-15)
list price: US$97.00 -- used & new: US$75.48
(price subject to change: see help)
Asin: 0898714540
Average Customer Review: 4.5 out of 5 stars
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Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.

The textbook contains more than 240 examples, 650 exercises, historical notes, and comments on numerical performance and some of the possible pitfalls of algorithms. It comes with a solutions manual that includes complete solutions to all of the exercises. As a bonus, a CD-ROM is included that contains a searchable copy of the entire textbook and all solutions. Detailed information on topics mentioned in examples, references for additional study, thumbnail sketches and photographs of mathematicians, and a history of linear algebra and computing are also on the CD-ROM, which can be used on all platforms.

Students will love the book's clear presentation and informal writing style. The detailed applications are valuable to them in seeing how linear algebra is applied to real-life situations. One of the most interesting aspects of this book, however, is the inclusion of historical information. These personal insights into some of the greatest mathematicians who developed this subject provide a spark for students and make the teaching of this topic more fun. ... Read more

Customer Reviews (26)

4-0 out of 5 stars Good depth and breadth
This is a good overall book that goes beyond your basic linear algebra texts such as Leon. If you're on the fence about buying it, just google Carl Meyer. His website has a digital copy of the text, so you can check it out and decide if it's worth buying. I commend the author for making the digital copies available, which is uncommon for an author to do. So if you find the text useful, please buy it!

Oh, by the way, the textbook includes a cd with searchable pdf copies of the book and solutions manual. That alone sets this text apart from most others.

3-0 out of 5 stars good for some, not so good for others
UPDATE: I decided to rewrite this since people didn't find it very helpful initially. This book was getting outstanding ratings across the board so I wanted to offer a different perspective. I used it for a Linear Algebra class, and I found the book to be fair, at best. The book attempts to strike a balance between proofs and practical applications. In that sense, it is a fairly balanced book, and in that same sense, it is lacking in both.

It is not a proof-oriented book. I prefer proof-oriented books like Axler and Lang. Although there are some proofs throughout the text, they are inconsistent. I had a few instances where I thought that obvious steps were missing (yes this happens frequently in math texts), and in one bizarre case I remember reading a poof whose theorem had never been stated! (This should have been picked up in the edit.)

As for the practical application side, we didn't delve deeply in my course. The practical applications are sprinkled throughout, but they are not the main focus. The main focus is on solving linear algebra problems that will be practically useful. The book does a solid job of presenting an array of problems, but it is not drill and kill. Still, more examples would have been helpful.

The notation is very modern. The reading I found mediocre. The solutions manual is good. Ultimately, I wanted to like this book more than I did. This text is reasonable for a third year undergraduate course looking at Linear Algebra from a broad perspective. You will have to think to use this text, and that's a good thing.

5-0 out of 5 stars A Remarkable Book of The Highest Standard
This outstanding book really defines a gold standard by doing so many things so well. I had used this book for a detailed self-study, and I couldn't be happier with the experience.

As an introductory text, it starts with the very basics. But it builds into a very detailed and comprehensive volume while progressively raising the level of mathematical rigor.

I think few books pay such meticulous attention to perfectly ordering every bit ofinformation such that the text is always absolutely concise, clear, and authoritative - without the slightest hint of forward reference or "hand-waving".

This book is densely packed with a large number of thoughtfully created examples and exercises that blend beautifully into the thread of the book. The majority of them illustrate applications of the ideas. Some others are referred to in later chapters as building blocks of proofs or simply motivate more advanced studies.

Every one of the end-of-chapter exercises is solved - or more accurately - worked out in complete detail in the accompanying solutions booklet. Quite extra-ordinary!

BTW, these examples and exercises are also the key to potentially pruning your study. The author warns in the preface that "this book is a comprehensive work that is not meant to be devoured cover-to-cover".

Finally, I like the book's simple and thoughtful typographical work. It makes effective use of indentation, partition lines, highlights and fonts - without creating distracting "visual noise" the way some modern text books seem to do!

1-0 out of 5 stars Most Useless Linear Algebra Book Ever Written
Not sure what the hype is over this book.It is "easy" to read, but it doesn't lay a solid foundation for further study in advanced linear algebra.Perhaps thats why the word "applied" is in the title; to be sure, all I learned from this book (I read perhaps three chapters before dumping it) were a few computational tricks. To be fair, I had an equally useless teacher who did his best to prove theorems which were not in the book (thereby rendering a good chunk of the book totally irrelevent).As far as the actual content of the book goes, the problems at the end of each section were either too hard or too easy.Generally speaking, there was no pattern to them (hence, you could do all the problems at the end of the section, and be left with very little conceptual understanding).The extremely terse solutions manual provided by the author did not help at all. In all honesty, I cannot say this book was at all motivating.

5-0 out of 5 stars Excelent book!
This is probably the best book to learn linear algebra from. The exposition is very clear and it has many insightful exercises. In my opinion, it contains everything that should be covered in an introductory course. ... Read more

19. Linear Algebra (2nd Edition)
by Kenneth M Hoffman, Ray Kunze
Hardcover: 407 Pages (1971-04-25)
list price: US$141.33 -- used & new: US$59.99
(price subject to change: see help)
Asin: 0135367972
Average Customer Review: 4.0 out of 5 stars
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Product Description

This introduction to linear algebra features intuitive introductions and examples to motivate important ideas and to illustrate the use of results of theorems.


Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms


For all readers interested in linear algebra.

... Read more

Customer Reviews (20)

5-0 out of 5 stars Bible on the subject
I have used this book as the textbook for a Linear Algebra discipline. It is considered the "reference" for that discipline in my institute. Although it can be considered the bible on the subject it should not be used alone in a first course of that subject, it is definitely not an introductory book. On the other hand, for a trained student or researcher on the subject it is simply one of the best (if not the best).

5-0 out of 5 stars The Evolution of Linear Algebra
As a professor of mathematics, I was recently assigned a section of our undergraduate linear algebra course;the last time I taught the course was twelve years ago. While doing the obligatory search for a course text, I have been surprised to see how the first course in linear algebra for mathematicians and scientists has "evolved" since I last taught it, at least insofar as that evolution is reflected through available and popular textbooks.

In one of the more popular linear algebra texts currently on the market (I will refrain from naming it), the formal definition of a vector space does not even occur until page 198, and this is not atypical.Looking through half a dozen of the more popular texts, one finds lengthy introductory chapters on vectors in R^n and their properties, basic matrix algebra, systems of linear equations,special algorithms for computing determinants and matrix inverses in efficient time, and significant space devoted to special matrix factorizations, such as the LU factorization.I would like to point out, without passing judgment, that this has not always been the case.Over time, the undergraduate course in linear algebra for mathematicians and scientists has evidently acquired a partial resemblance to the computational, non-proof-based course in "Matrix Algebra" that used to be offered to "casual users" of this area of mathematics at nearly all major universities.

Hoffman and Kunze's book was written for the undergraduate linear algebra course at MIT in the 1960s.Those of us who pursued graduate study in mathematics in the 1970s saw copies of this text, with its vivid purple stripes down the cover, on the shelves of virtually every serious graduate student.Simply put, Hoffman and Kunze was a "standard" undergraduate reference for decades, which continued to inform its readers well into graduate programs or professional careers.

The author of this review did not have the good fortune to use Hoffman and Kunze in a course, but I always had a copy at hand as a reference.My first linear algebra course, taken as a sophomore in the 1970s, used a text by Robert Stoll and Edward Wong (Academic Press, 1968).In Stoll and Wong, the definition of a vector space occurs on page 4, not on page 204.There is no preliminary chapter on basic matrix algebra;these computations are discussed as they arise, in context, when one chooses a basis for a vector space and therefore places coordinates on that space.The entire organization and conceptual structure of Stoll and Wong's book is worlds apart from the texts I have been reviewing of late.The same may be said of Hoffman and Kunze, and indeed of most of the popular linear algebra books from that period of time.This is why I am a bit disturbed when I read reviews that declare Hoffman and Kunze's classic text "outdated," "irrelevant," or "impossible to read."If the younger reviewers are comparing Hoffman and Kunze to most of the popular competitors that have been published in the past five years or so, then they are comparing a remnant apple to a crate of newly harvested oranges.

Against all odds, Hoffman and Kunze remains in print, 46 years after its first apperance.And this in an era when the typical college text remains in print for what seems like less than five years.There is a reason for this longevity.For serious students of mathematics and the mathematical sciences, this text remains invaluable.If one is going to be called upon to actually USE linear algbra in any substantive way (and by substantive I do not mean inverting a matrix or solving a system of two linear equations in two unknowns), then one eventually must learn about such things as dual spaces and double duals, cyclic decompositions and the Jordan canonical form, unitary operators, self-adjointness, the spectral theorem, and multilinearity and tensors. One cannot even find most of these topics in the most popular undergraduate texts currently available on the market;they appear to reach their summit when they discuss eigenvalues and eigenvectors.As a consequence, if a student in an advanced course in, say, differential geometry or differential equations is sent back to his or her linear algebra text to read about dual spaces or the Jordan canonical form, then it will be necessary to abandon the text with which he/she is familiar and refer to a more serious reference like Hoffman and Kunze.How terribly inefficient.

In the spirit of fairness, I must observe that the text Linear Algebra, 4th ed., by Friedberg, Insel and Spence is a currently available undergraduate text that is comparable to Hoffman and Kunze in coverage and rigor.It is an excellent text for a first course for mathematics majors---a true anomaly among a host of weaker competitors.However, the authors may dissuade many would-be users by their declaration in the preface that their text is "especially suited for a second course in linear algebra that emphasizes abstract vector spaces, although it can be used in a first course with a strong theoretical emphasis."The second undergraduate course in linear algebra is evidently becoming increasingly common;is this because the first course has been weakened to "matrix algebra" and therefore leaves the student unprepared to cope with advanced mathematical courses?

My sincere thanks go out to Prentice-Hall for keeping Hoffman and Kunze in print all these years.Linear algebra is the essential prerequisite for nearly all advanced mathematics, and it is good to see that at least one definitive reference remains available, even as market and societal forces in higher education bring about a clear, demonstrable devolution in the quality of introductory texts on the subject.

5-0 out of 5 stars Linear Algebra
This book is very rigorous and detailed. This book covers what usually is covered in 2 semesters of Linear Algebra, it covers introductory and advanced Linear ALgebra. I would not recommend it for someone who has not ever seen Linear Algebra because of the lack of concrete examples although I would highly recommend it for someone who has had Linear Algebra. This book is all the Linear Algebra you need up to a Master's degree in Mathematics. For Linear Algebra beginners I would recommend the following 2 books because no one book is good enough : "Elementary Linear Algebra" by Robert S. Johnson; and "Linear Algebra 3rd edition" by Fraleigh. Please see also "Linear Algebra, an applied first course 8th edition" page 447 for those of you intersted in Differential Equations.

5-0 out of 5 stars A Beautiful Mathematics Book
A comphrensive introduction to the subject of linear algebra that every undergraduate should read. This book explains in detail the concepts that make up linear algebra and will be enjoyed immensely by anyone with an intrest in pure mathematics. Of course, since it is written from a pure point of view, the authors have made almost no mention of practical applications. This is a book soley for the mathematics student. This book has had a wonderful and profound impact on my views of mathematics and I can only give my heartfelt thanks to the authors for writing such a beautiful book. If you have an intrest in linear algebra and operator theory, buy this book! You will have a blast exploring the realm of pure mathematics and thank yourself later.

5-0 out of 5 stars A unique approach
This was the textbook they used to use at MIT in the past few decades. Virtually, however, nobody uses this book in a regular undergraduate course anymore. Instead of developing the ideas in the familiar context of the real numbers, Hoffman and Kunze give a more abstract (and general) discussion. For example, the theorems about determinants work in all commutative rings. The rigorousness and the wealth of information are overwhelming for most undergraduates to handle. You will not learn anything if you just glance through the pages. Every line requires deep thought. Down-to-earth applications are not included. So I do not recommend this book for engineers. ... Read more

20. Applied Numerical Linear Algebra
by James W. Demmel
Paperback: 431 Pages (1997-08-01)
list price: US$75.50 -- used & new: US$70.78
(price subject to change: see help)
Asin: 0898713897
Average Customer Review: 4.5 out of 5 stars
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Product Description
Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations.

If you are looking for a textbook that - teaches state-of-the-art techniques for solving linear algebra problems, - covers the most important methods for dense and sparse problems, - presents both the mathematical background and good software techniques, - is self-contained, assuming only a good undergraduate background in linear algebra,

then this is the book for you.

Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in Matlab and are freely available on the Web.

Material either not available elsewhere, or presented quite differently in other textbooks, includes - a discussion of the impact of modern cache-based computer memories on algorithm design; - frequent recommendations and pointers in the text to the best software currently available, including a detailed performance comparison of state-of-the-art software for eigenvalue and least squares problems, and a description of sparse direct solvers for serial and parallel machines; - a discussion of iterative methods ranging from Jacobi's method to multigrid and domain decomposition, with performance comparisons on a model problem; - a great deal of Matlab-based software, available on the Web, which either implements algorithms presented in the book, produces the figures in the book, or is used in homework problems; - numerical examples drawn from fields ranging from mechanical vibrations to computational geometry; - high-accuracy algorithms for solving linear systems and eigenvalue problems, along with tighter "relative" error bounds;- dynamical systems interpretations of some eigenvalue algorithms.

Demmel discusses several current research topics, making students aware of both the lively research taking place and connections to other parts of numerical analysis, mathematics, and computer science. Some of this material is developed in questions at the end of each chapter, which are marked Easy, Medium, or Hard according to their difficulty. Some questions are straightforward, supplying proofs of lemmas used in the text. Others are more difficult theoretical or computing problems. Questions involving significant amounts of programming are marked Programming. The computing questions mainly involve Matlab programming, and others involve retrieving, using, and perhaps modifying LAPACK code from NETLIB. ... Read more

Customer Reviews (18)

3-0 out of 5 stars It's Pretty Good, but Definitely Needs a Good Instructor to Supplement It
This is a fairly good, concise analysis of numerical linear algebra. It covers topics in a logical manner and overall has fairly good explanations. However, I feel that it has a few notable shortcomings.

Although explanations are fairly good, I found that they were too short. A minimum amount of detail is given, and there are very few examples. Also, there are very few end-of-chapter problems, and the ones given are almost all quite difficult and there are no answers available.

For these reasons I would only recommend this book for people with a strong background in linear algebra. I was an engineering undergraduate with a limited knowledge of linear algebra when I read it, but an upper-year math major or a math graduate would probably find this book to be ok, as long as their course instructor gives many supplementary resources, such as practice problems.

4-0 out of 5 stars Excellent for its purpose
I am reviewing the book by Trefethen not by Demmel.There has been some confusion about these two books.

Many people commented that this book is logic and easy to read.Compared with some other books, this is true.However, the perquisite for this book is a sound understanding of linear algebra.Without that, you will need to be a math genius to find this book easy to read.So, this is an excellent book for your (at least my) first exposure to numerical linear algebra.It picks up about 40 important topics and cover them in such details that are not too overwhelming.

With the above positive side, I wish the author could expand the book and cover more topics or some topics in greater details.This book is good for an one semester course (Note that it has only just more than 300 pages for the main content).Many books are easily enough for two courses if not more.So, as a text book, this is excellent.But as a reference, you will need another book to go with it.Unfortunately, other books are not so easy to read.

By the way, for CG method the book is not excellent. You will need the article by Jonathan Richard Shewchuk. You can find it online. This is the best for CG.

5-0 out of 5 stars It couldn't be better
Beautiful! Very simply, if you want to have an insight on linear algebraic procedures, and why this and that happens so and so, this is the book. Topic-wise, it is almost complete for a first treatment. Each chapter starts with a gentle introduction, building intuition and then gets into the formal material. The style is solid.

Although talking about procedures, it also attempts to give some geometric intuition here and there. It helps.

This is not a reference book though. You cannot find every important procedure.

5-0 out of 5 stars Good reference
I have been using this textbook for my Numerical Linear Algebra class, and it have been a great help, actually is a good complement to Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III. I totally recommend it.

5-0 out of 5 stars Great Book for Self-Learning
I am a second year PhD student in Operations Research and for long I had been looking for a book in linear algebra to help me learn it myself (as I see that I need it no matter what research I want to do. It's just a good tool to know). One of my friends recommended this book to me, I got it and I am very happy with it. The book is great in different ways:
-it is in the form of short lectures and for me who wants to learn linear algebra step by step, this is a perfect approach. You will have a 5-6 page lecture so whenever you start, you are set to finish that lecture.
-It gives you intuition and understanding about what is really happenning geometrically which is amazing. To me, it is very important to have the "feeling" of what is happening because it is only then that you can think about bringing your real problem in this framework.
-The examples in lectures clarify the subject while exercises give you a chance to learn even more.
If you are new to linear algebra or know it but want to refresh your mind on intuitions and systematic thinking, I highly recommend this book. ... Read more

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