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21. Matrices and Linear Algebra (Dover
22. Introduction to Linear Algebra
23. Linear Algebra: An Introductory
24. Applied Linear Algebra (3rd Edition)
25. Schaum's Easy Outline of Linear
26. Linear Algebra Problem Book (Dolciani
27. Linear Algebra and Its Applications
28. Introduction to Linear Algebra
29. Elementary Linear Algebra with
30. Numerical Linear Algebra and Applications,
31. Linear Algebra (4th Edition)
32. Advanced Linear Algebra (Graduate
33. Student Solutions Manual for Differential
34. Elementary Linear Algebra with
35. Advanced Linear Algebra for Engineers
36. The Linear Algebra a Beginning
37. Student Solution Manual for Linear
38. Elementary Linear Algebra
39. Elementary Linear Algebra
40. Linear Algebra (Undergraduate

21. Matrices and Linear Algebra (Dover Books on Advanced Mathematics)
by Hans Schneider, George Phillip Barker
Paperback: 432 Pages (1989-06-01)
list price: US$16.95 -- used & new: US$3.99
(price subject to change: see help)
Asin: 0486660141
Average Customer Review: 3.0 out of 5 stars
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Product Description
Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues and differential equations. Numerous exercises, both true-false and multiple choice, with each chapter. Answer section.
... Read more

Customer Reviews (8)

2-0 out of 5 stars Terrible
this book is terrible, it's confusing and lack of explaination, i recommand u to get the Linear Algebra and it's application by Davie C. Lay

1-0 out of 5 stars Worst Math book ever run away!
This is the text book for a linear Algebra class and I really wish I dropped the class because of the book. It's not student friendly because of poor and incomplete discussion of the subject and slim to no examples in the book wit few exercises and even less answers in the back. The book is cheap at around 16.00 but that is to high of a price for poor presentation of the material.

4-0 out of 5 stars Cheap, formal, well written
On my desk right now, books by: David C. Lay, Terry Lawson, Sheldon Axler, Klaus Jänich, Robert Valenza, and this one by Schneider and Barker. I tend to go back again and again here.
I'm using this book as a supplement for the textbook in my class. Some of the books cited above don't quite fit the bill because they're so different from the linear algebra for engineering you so often see in classes. But this one is excellent for a matrix-heavy approach.
This book is "bare bones", indeed, but it is very well written. Some might not be used to definitions, propositions, theorems and lemmas but in this case this makes it a whole lot easier for finding (and referencing) the important results. The notation is careful and formal, but the explanations are crystal clear. On the back cover it says it's geared towards students "outside the field of mathematics" but I think they say that because it avoids a purely algebraic approach (like in Valenza where e.g. Ker is defined in the context of group homomorphism). The approach is the one of matrixes, matrixes everywhere (row echelon algorithm, etc.) There are, however, no "modern" applications (such as networks, or ecology) as examples.
Another reviewer complained about the difficulty in exercises. While you have "drill" ones, you do have more conceptual ones, but I think they're on par with the text. There are no pretty illustrations here, and you will see that you don't need them.
In some other books, material might be presented in a wordy manner, but in this book, you just say "ah, so what so-and-so is saying is just Theorem number X.X.X in S&B."
On the whole, this is an excellent acquisition for your undergraduate library. It is cheap and good. What more do you want?

2-0 out of 5 stars Surf the web instead.
For about three years, I haven't thought about linear algebra at all.But recently, I've been interested in it again, and went to this book for reference.

I'm lucky if I can find one nice clear example of anything in this book.This is a proof book all the way, and it's not for your general type of audience.This is bare bones stuff.That's probably why the price is 14 bucks instead of 140.

Instead of getting a book like this, I recommend getting a more expensive book that's easier to understand, or just surf the internet for information.I have had some success with the latter option.

5-0 out of 5 stars Supplemental Superiority
As a physics major, i've been told by my E & M teacher that Linear Algebra is one of the two games to be played in physics. (The other naturally being calculus). So, what happens when it comes time to take Linear Algebra and the teacher only serves to confuse the material, and the college textbook is a normal college math book? (a.k.a. not well written or useful). Get Dover books. And this book delivers for me. Everything i'm supposed to learn in Shifrin's text is presented here with much clearer writing. (Especially in drawing your eye to the thereoms, any one who wants to Linear Algebra without knowing the thereoms or applying them to the homework should probably stop now and go back to Trig.) It seems this book would make a good stand alone text, provided you are willing to not expect calculus cookbookness, because it's my side text that trumps my main textbook for 1/10th the price. And in closing, thank God for Dover for making life as a physics major that much cheaper. ... Read more

22. Introduction to Linear Algebra (Undergraduate Texts in Mathematics) 2nd edition
by Serge Lang
Hardcover: 293 Pages (1985-12-19)
list price: US$74.95 -- used & new: US$47.20
(price subject to change: see help)
Asin: 0387962050
Average Customer Review: 3.5 out of 5 stars
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Editorial Review

Product Description
This book is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, and others are conceptual. ... Read more

Customer Reviews (11)

1-0 out of 5 stars Missing Pages
I started using this book as it was the assigned for a course. However, it's mid-semester, and I realized my book is missing pages! I'm pretty sure it's a binding issue....

I'm very disappointed, and it's a huge annoyance to pay for a textbook that is missing pages. I wanted to study for an upcoming an exam, but will have to borrow a friend's book in the meantime. Do not buy this book, get the hard-copy book if possible.

5-0 out of 5 stars A good math textbook
This book is easy to understand, and very concise.There are a few printing errors, but I'm pleased with it.The answers are in the back of the book, but sadly no hints or detailed solutions.My professor chose to provide those as additional course materials, which I have found helpful.

Overall, a better than average math text.

4-0 out of 5 stars A nice introduction for students of pure mathematics.
Serge Lang's Introduction to Linear Algebra provides a nice introduction to the subject.The text, which is designed for a one semester course for students whoare taking or have completed multi-variable calculus, covers the basic theory and computational techniques.Since the emphasis is on proving theorems rather than the applications that are of interest to physical scientists, engineers, and economists, the text is best suited to pure mathematics students.

Topics are motivated, the theory is carefully developed, computational techniques are demonstrated through clearly written examples, and geometric interpretations of the algebra are discussed.The exposition is generally clear, but I occasionally had to turn to Blyth and Robertson's Basic Linear Algebra 2nd Edition or Friedberg, Insel, and Spence's Linear Algebra (4th Edition) for clarification when examples were lacking (notably in the section on eigenvalues and eigenvectors that precedes the introduction of the characteristic polynomial).Another caveat is that there are also numerous errors, including some in the answer key.

The exercises consist of computational problems, which require meticulous attention to detail, and proofs of results that extend the topics developed in the text. The exercises are organized thematically in order to teach concepts not covered in the body of the text. Some problems are reintroduced after additional material has been developed, so that you can solve them in new, more efficient, ways, thereby demonstrating the power of the new techniques that you are learning.Answers to most of the exercises are provided in an appendix, making the text suitable for self-study.

The text begins with a review of vectors.This material is drawn from Lang's Calculus of Several Variables (Undergraduate Texts in Mathematics) and should be familiar to most readers.Next, Lang demonstrates how matrix algebra can be used to solve systems of linear equations.While the reader presumably learned how to solve systems of linear equations in high school (or even earlier), the discussion of homogeneous linear equations, row operations, and linear combinations provides the foundation for subsequent topics in the book.

The remainder of the book is devoted to finite-dimensional vector spaces.Once Lang introduces the basic definitions, he covers linear independence, the basis of a vector space, and dimension.This leads to a discussion of linear mappings, their representation by matrices, and how the kernel and image of these maps are related to the rank of the matrix of linear transformation.Lang discusses composition of mappings and inverse mappings before delving into scalar products, orthogonal bases, and bilinear maps.Lang then develops the theory of determinants and discusses how to apply them to solving systems of linear equations, finding the inverse of a matrix, and calculating areas and volumes.After introducing eigenvectors, eigenvalues, and the characteristic polynomial, Lang concludes the book with a discussion of the eigenvectors and eigenvalues of symmetric matrices that uses the earlier material on scalar products and orthogonality.

Much of this material is drawn from Lang's Linear Algebra (Undergraduate Texts in Mathematics), where it is treated in more depth.However, that text is written for students already familiar with basic matrix manipulations, so it does not discuss elementary matrices or Gaussian elimination.Understanding it also requires greater mathematical sophistication.

This text is limited in scope.If you are preparing to do graduate work in mathematics, you will need to read an additional text such as Lang's Linear Algebra, Friedberg, Insel, and Spence's Linear Algebra, Hoffman and Kunze's Linear Algebra (2nd Edition), Axler's Linear Algebra Done Right, or Blyth and Robertson's Further Linear Algebra.Of these, the one that is most suitable for self-study is Further Linear Algebra.

If you are interested in an introductory text that is suitable for self-study, you may wish to consider Blyth and Robertson's Basic Linear Algebra as an alternative to this one, as it includes abundant examples and answers to almost all the exercises.

2-0 out of 5 stars Marginal Text
I used this book for a college-level linear algebra course and found it marginal. Although the author is clear, he skips steps and does not provide ANY answers to exercises in the back of the book. Sometimes you can find the answers to exercises in proofs contained in subsequent chapters. You really need a good professor (which I thankfully had) to get the most out of this course and book.

3-0 out of 5 stars Too Concise (3.5 Stars)
This book was used in our intro to linear algebra for math/physics majors, and it was decent, but not great.The book is very concise, so you can easily read it before your lecture and then again after lecture (most sections are about 5 pages).However, this also leads to some things not being hammered in, or not emphasized as much as they should be.Also, there are very few examples of actual problems, and the reader is often left having to do something concrete from the theory with no examples.This is a tad annoying, but is good in that it makes you think.However,there are a few errors in the answers in the back of the book.So there were a few times I did what I thought was the logical way to do a problem, and my answers were not the same as the books, but mine were correct.These errors in the book were very annoying, but the actual text, for the most part, had few errors.The style of writing is fine, and to the point.

Overall, the book is decent, but I am sure there are better books out there. ... Read more

23. Linear Algebra: An Introductory Approach (Undergraduate Texts in Mathematics)
by Charles W. Curtis
Hardcover: 364 Pages (1984)
list price: US$69.95 -- used & new: US$35.00
(price subject to change: see help)
Asin: 0387909923
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
This revised and updated fourth edition designed for upper division courses in linear algebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linear algebra and calculus are worked into the discussion. A special feature is the inclusion of sections devoted to applications of linear algebra, which can either be part of a course, or used for independent study, and new to this edition is a section on analytic methods in matrix theory, with applications to Markov chains in probability theory. Proofs of all the main theorems are included, and are presented on an equal footing with methods for solving numerical problems. Worked examples are integrated into almost every section, to bring out the meaning of the theorems, and illustrate techniques for solving problems. Many numerical exercises make use of all the ideas, and develop computational skills, while exercises of a theoretical nature provide opportunities for students to discover for themselves. ... Read more

Customer Reviews (8)

3-0 out of 5 stars Terse text but easy exercises
As other readers have noted, this is your standard, terse, theorem-lemma-proof type math text.If you are approaching this text with your only mathematical background being a popular treatment of the calculus like those of Stewart or Larson, the style takes a lot of getting used to.Though a lot of effort is placed into making the text short and packed with information, it is impossible to sit down with this text (or any other upper-division math text, for that matter) and read passively.Curtis leaves out many details in the proofs and examples, asking the reader to follow the ordinary, though annoying, convention of theorem-lemma-proof texts and provide the details him(yes, him)self.

In my linear algebra class, we covered the equivalent of the first six chapters, though after the determinants chapter, we stopped following the ordering and pace of the text, and therefore, it's hard to tell whether the later chapters make an optimal teaching or self-study device.The first four chapters (up to determinants), however, take a theoretical approach to linear algebra with a few scattershot references to the geometric intuitions that it formalizes.

My biggest complaint is that in some points of the text, Curtis seems unsure of whether to continue in an informal or an abstract manner.Many of the exercises are numerical problems of the type you see in a non-proof linear algebra class focused on applications, and when Curtis gets to systems of linear equations, he seems confused about whether he is writing a book for a proof-based or a numerical class.As long as you are familiar with induction and proof by contradiction, the exercises that require proofs are fairly easy.Our professor constantly supplemented them with problems that were far more difficult than anything in Curtis.

5-0 out of 5 stars Good Book for Introductory Linear Algebra
This is a fantastic resource for basic linear algebra. It covers the topics from a rather theoretical perspective, which lacks many examples or practical applications, but presents the theory better than most alternate books. The book does include some applications/advanced theory moving past the basic topics of solutions of systems, vector spaces, linear transformations, determinants, and orthogonality, which includes solving differential equations and basic symmetry theory. The book is short and sweet, which is good if you can handle more advanced math textbooks, but not good for those looking for detailed explanation (some of the proofs of basic concepts are even left up to the reader when appropriate). This book is better for those already familiar with the subject matter or those looking for a challenge.

4-0 out of 5 stars Used for Self Study
I used this book for an independent study of linear algebra in undergrad.I'd had no prior exposure to the field, but had taken very good real analysis and abstract algebra courses prior.My self-study was quite effective, which is a testament to the book, since it was essentially the only material I had.(There were a few typos I remember seeing, as well as some unclear formulas/notation here and there, hence the four stars, but nothing serious).

5-0 out of 5 stars Beautiful Work
I used this book for a first course in linear algebra at Ohio State University and I could not have been more satisfied.It is a challenging book to use, but very rewarding for those who put the time into it.

3-0 out of 5 stars OK, but could be better.
The book sometimes eliminates using some symbols when the meaning is clear from the context; this is OK only if you either have prior understanding of the material presented or easy access to an expert. ... Read more

24. Applied Linear Algebra (3rd Edition)
by Ben Noble, James W. Daniel
 Paperback: 521 Pages (1987-11-11)
list price: US$84.00 -- used & new: US$61.00
(price subject to change: see help)
Asin: 0130412600
Average Customer Review: 4.5 out of 5 stars
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Product Description
This classic volume applies linear algebra to a variety of disciplines–engineering, the physical sciences, social sciences, and business. It motivates the reader with illustrative examples. This is a competitor to Strang.
... Read more

Customer Reviews (3)

4-0 out of 5 stars Less abstract than many
Not as abstract as many linear algebra books, with less emphasis on proof and more on understanding how the pieces fit together.

5-0 out of 5 stars Favorite Linear Algebra Book
This is one of the best math books I have ever read. I had to learn linear algebra for my graduate research and this book was invaluable. I just wish they wrote a differential equations book as well. The best part of this book are the excellent conceptual explainations, but the proofs are well motivated and clear as well, and I usually hate proofs. The coverage of Singular Value Decomposition is very good.

5-0 out of 5 stars Best text for undergraduates on Linear Algebra
It provides an excellent approach to Linear Algebra for self-pacing. Different from other linear algebra books, it's well organized and teaches how and why the ideas come from by providing many interesting examples.

It isn't only the classics, but the essential reference for related fields in my bookshelf. ... Read more

25. Schaum's Easy Outline of Linear Algebra
by Seymour Lipschutz, Marc Lipson
Paperback: 160 Pages (2002-08-12)
list price: US$11.00 -- used & new: US$3.69
(price subject to change: see help)
Asin: 0071398805
Average Customer Review: 3.5 out of 5 stars
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Product Description
Boiled-down essentials of the top-selling Schaum's Outline series for the student with limited time

What could be better than the bestselling Schaum's Outline series? For students looking for a quick nuts-and-bolts overview, it would have to be Schaum's Easy Outline series. Every book in this series is a pared-down, simplified, and tightly focused version of its predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form.

Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.

  • Designed to appeal to underprepared students and readers turned off by dense text
  • Cartoons, sidebars, icons, and other graphic pointers get the material across fast
  • Concise text focuses on the essence of the subject
  • Delivers expert help from teachers who are authorities in their fields
  • Perfect for last-minute test preparation
  • So small and light that they fit in a backpack!
... Read more

Customer Reviews (4)

4-0 out of 5 stars Good introduction
If you're new to linear algebra, this book may clarify some concepts in a traditional textbook. If you understand your college text ok or are looking for a more in depth study, this is not the book for you. I found it to be helpful and easy to understand.

2-0 out of 5 stars Kindle version.Too many examples unreadable due to formating problems
This is a review of the kindle version.As this book attempts to convey a large amount of information in a small book, it relies heavily on the examples.I normally like this form of teaching as it helps me understand the concepts.The problem is that in the kindle version, a large number of the examples are scrambled.This makes it much harder to understand the text as it refers to the example.Not all of the examples are this way, but around 1/3 of them are so far.I stopped at around 80% of the way through.

3-0 out of 5 stars Not what i'd hoped for
This book gives you the theorems, with examples of how to use the theorems.However i was disappointed because i was hoping to that it would make linear algebra clearer for me.Specifically, i was hoping for proof's of the theorems, which this book doesn't contain.It is a good reference book to look things up in, but not a book for obtaining a deeper understanding.

5-0 out of 5 stars Great study guide / reference book!
I really, really don't like learning mathematics, but unfortunately some maths is required by my university's computer science course.

If you're a person like me who can't understand any of the stuff in your mathematics professor's cryptic notes, then I strongly advise you to buy this book. It's very easy to read (for a maths book), has examples explaining everything, and it's dirt cheap compared to the hardcore maths books out there which often contain too much information for a (undergraduate) student's needs! It has made studying and understanding linear algebra easy (as the title says), and it also got me through the exam the first time.

Here's what this book covers:

Chapter 1: Vectors in Rn
Chapter 2: Algebra of Matrices
Chapter 3: Systems of Linear Equations
Chapter 4: Vector Spaces
Chapter 5: Inner Product Spaces; Orthogonality
Chapter 6: Determinants
Chapter 7: Diagonalisation: Eigenvalues and Eigenvectors
Chapter 8: Linear Mappings
Chapter 9: Canonical Forms

(this little book is, unlike the information given here, 156 pages long) ... Read more

26. Linear Algebra Problem Book (Dolciani Mathematical Expositions)
by Paul R. Halmos
Paperback: 350 Pages (1996-09-05)
list price: US$47.95 -- used & new: US$42.47
(price subject to change: see help)
Asin: 0883853221
Average Customer Review: 4.5 out of 5 stars
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Product Description
Can one learn linear algebra solely by solving problems? Paul Halmos thinks so, and you will too once you read this book. The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way ofa series of 164 problems, each with hints and, at the back of the book, full solutions. This book is a marvelous example of how to teach and learn mathematics by 'doing' mathematics. It will work well for classes taught in small groups and can also be used for self-study. After working their way through the book, students will understand not only the theorems of linear algebra, but also some of the questions which were asked which enabled the theorems to be discovered in the first place. They will gain confidence in their problem solving abilities and be better prepared to understand more advanced courses. As the author explains, 'I don't think I understand a subject until I know the questions ... I wrote this book to organize those questions, problems, in my own mind.' Try this book with your students and they too will be able to organize and understand the questions of linear algebra. ... Read more

Customer Reviews (6)

4-0 out of 5 stars Text is great, printing is not
This is an absolutely excellent book. I came at it before I had ever taken a linear class. The book develops the subject in a way that it seems a natural progression. I was never faced with a proof that seemed to be just number crunching; they all get at the very heart of what is at stake. I recently read back through it after taking a linear class, and I still come to a better understanding of the subject by looking through this. It is well worth your time. The only complaint I have with the book is that there are a lot of typos. It frequently refers back to the wrong problem number, and there are typos in the mathematics that could cause problems if you aren't keeping track of what is happening. (Ex: in the solution to 135, they forget to specify orthogonal projections, or in 145 they say that if y=Px then what is wanted is Uy=Px when it should actually read Uy=Ax) The text is written clearly enough you should be able to figure out what is happening, but if another edition comes out it would be worth upgrading

3-0 out of 5 stars Not as good for second year graduate students
It is a good book for beginners but not as great for graduate students.

5-0 out of 5 stars Great book!
I agree with the following reviewer in that Halmos' books are always entertaining and inviting! Fun to read, concise yet clear! The book contains most of the elementary yet important problems in an undergrad course with solutions in the back. It's very helpful working through all these problem because it will tremendous enhance your understanding of the subject. Also, if you want a hardcore problem oriented approach to linear algebra, check out Proskuryakov's Problems in Linear Algebra. Some of the problems in the book are Putnam like. Virtually any type of Putnam taste problems in Linear Algebra can be found in Proskuryakov.But this one, contrast to Halmos', is the least entertaining--that's why it is called HARDCORE PROBLEM APPROACH! You would be a great linear algebra problem solving machine working through both books!

5-0 out of 5 stars Start out with one of the best
Halmos is one of the great mathematical expositors of the 20th Century, and his book "Finite Dimensional Vector Spaces" stands as the definitive introduction to the subject for budding mathematicians. This book, "Linear Algebra Problem Book", is perhaps best described as an engaging and semi-informal invitation and complement to that original work, which grew out of lectures given by the legendary John von Neumann. In contrast to typical treatments of linear algebra, "Finite Dimensional Vector Spaces" is abstract (introduces determinants through alternating forms), rigorous, concise, and demands a certain level of mathematical maturity. This book, "Linear Algebra" is exactly the opposite. Starting from very little assumed background, it all but gives away the store, written in plain language, anticipating students' questions and misconceptions, and leading them to a deeper understanding of mathematics through the Socratic method. This is not a problem book in the Schaum's outline sense; there is no drill or rote calculations. Every question is carefully chosen to illustrate a point or expose a potential misunderstanding in the student's knowledge or to exercise the student's intuition and ability to make connections. The answers are given as detailed explanations, integral to the exposition, which go far beyond merely answering the questions posed, raising deeper implications and questions. This is an excellent book for beginning students of higher mathematics, and a very user friendly guide to Halmos' classic text.

5-0 out of 5 stars Clear, interesting, easy to follow.
I'm no mathematician but, I own a number of linear algebra and abstract algebra books and this book makes them all pale in comparison. I really enjoyed working through it. Maybe a bit pedantic for more advanced typesbut, if you want to get a handle on the concepts this is the book. ... Read more

27. Linear Algebra and Its Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)
by Peter D. Lax
Hardcover: 392 Pages (2007-09-10)
list price: US$89.95 -- used & new: US$64.33
(price subject to change: see help)
Asin: 0471751561
Average Customer Review: 4.5 out of 5 stars
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Praise for the First Edition

". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.

Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.

Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:

  • The QR algorithm for finding the eigenvalues of a self-adjoint matrix
  • The Householder algorithm for turning self-adjoint matrices into tridiagonal form
  • The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space
Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices.

Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals. ... Read more

Customer Reviews (5)

5-0 out of 5 stars A good algebra book
I would recommend this book to those who have learned linear algebra long ago and plan to pick up some back.

This book gives an extremely concise introduction to the core of linear algebra(so not quite the best for beginners), without any redundant sentences in trivial calculation. Starting with linear map and ending in spectral resolution, different parts are united. It also advances with the times, include topics like duality, convexity, which is interesting from engineering perspective.

For those who only learn some elementary algebra in undergraduate, this book helps to make a big picture and to show some deep reason behind that.

4-0 out of 5 stars concise and elegant, and also covers Banach spaces
I would compare this book with Paul Halmos' classic "Finite Dimensional Vector Spaces". Both books cover much in common, both in material and style. Each is slender and gracefully written. Lax takes us through many of the simple results and methods of linear algebra. Unlike Halmos, this book also covers computational aspects. A nod to the ever increasing prevalence of computers. The theorems are proven in a rigorous fashion. But with some attention, you should be able to follow the logic.

Lax also provides a discussion of Banach spaces - complete normed spaces. Whereas other linear algebra texts might focus more on Hilbert spaces, which are complete inner product spaces. The inner product is bilinear, which leads to easier analysis than for normed spaces. Which is perhaps why Banach spaces are typically not as well covered.

5-0 out of 5 stars Excellent Graduate Presentation of Linear Algebra
I used to hate this book but it was due to inadequate presentation at the time I was first introduced to it.Over time it has become my favorite Linear Algebra text.Use Axler's "Linear Algebra Done Right" then move up to this text.Being able to do linear algebra at this level is crucial to anyone doing advanced mathematics, science, and engineering.Be sure to have it handy.

5-0 out of 5 stars My first math book without picturse and examples
I used Lax in my honor linear algebra class as a college freshman. With not much previous experience in abstract math, this book could be a bit frustrating. However, if you really strive to understand what each sentence really means, it's not all that difficult. This is a very concise book and at times I spent hours reading one page. My class didn't end up covering the whole book, but I finished it on my own the summer following my freshman year. Now I feel very confident about linear algebra and it led to my later more in-depth study in algebra.

4-0 out of 5 stars Best Linear Algebra Review Book
Linear Algebra is one of the most basic topics in science and engineering. Everyone takes an undergraduate course, but few science/engineering graduate students have mastery of the material upon entering grad school. Ifind that Lax's book is an excellent book to recommend to our graduatestudents for self review. The few but very well chosen topics and thestraightforward yet deep way they are covered make the book engaging,thought provoking, and easily followed by upper level undergrads andbeginning grad students. A student with a mastery of the material in thisbook will have little trouble with grad courses in the many engineering andscience courses that rely on linear algebra. ... Read more

28. Introduction to Linear Algebra and Differential Equations
by John W. Dettman
Paperback: 416 Pages (1986-12-01)
list price: US$16.95 -- used & new: US$4.00
(price subject to change: see help)
Asin: 0486651916
Average Customer Review: 4.5 out of 5 stars
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Product Description
Excellent introductory text for students with one year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order nonlinear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. 48 black-and-white illustrations. Exercises with solutions. Index.
... Read more

Customer Reviews (3)

3-0 out of 5 stars Only the first half is good
The first half of this book is good.Although Dettman does occasionally skip nonobvious steps, he does a good job of introducing the reader to complex numbers, matrices, and linear algebra.The second half, though, concerning differential equations is awful.I originally got this book to teach myself these two subjects over the summer and shortly into Chapter 5 I had to give it up and switch material; the explanation is murky and the presentation confusing:it only really makes sense after you go somewhere else and learn differential equations, then come back and look at it again.

If you want to learn linear algebra, you can't go wrong with this book, although there are better choices out there.If you want to learn differential equations, this is not the book for you.

5-0 out of 5 stars Good for reference or self study
The book is easy to read.Dettman manages to find an excellent balance between formal proof and informal explanation.The first two chapters on Complex Numbers and Linear Algebraic Equations are particularly good, and this has become the first book I usually reach for if I need to look up something about matrices.Matrix notation is used throughout the book for topics such as linear transformations and systems of equations.There are hints and answers to about half the exercises at the end of the book, making it very helpful for self study.

5-0 out of 5 stars Excellent for Physicists
I am a physicist, and as a sophomore in college I was warned by the juniors:"Learn linear algebra!!!!They hardly teach any of it in the required math classes, and you'll die in quantum without it!!!"So I studied this book.Even without doing many of the problems I got a clear grasp of what a vector space is, why it is more than mere formalism, what a linear transformation is, the significance of bases, diagonalization, and how to work with matrices and really understand them.All of this was indispensable in studying quantum mechanics.

Of course, solving the problems will only help your understanding.I HIGHLY recommend this for any physics student who had a bad (or non-existent) linear algebra class. ... Read more

29. Elementary Linear Algebra with Applications, Student Solutions Manual
by Howard Anton, Chris Rorres
Paperback: 265 Pages (2010-07-26)
-- used & new: US$48.37
(price subject to change: see help)
Asin: 0470458224
Average Customer Review: 3.0 out of 5 stars
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Editorial Review

Product Description
This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide variety of interesting, contemporary applications. This book contains clear, accessible, step-by-step explanations that make the material crystal clear. It establishes the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues. ... Read more

Customer Reviews (3)

2-0 out of 5 stars Not as comprehensive as I expected
The textbook itself I gave a high rating. I wouldn't bother with this solutions guide. It doesn't have many more solutions than what is alrady in the textbook. The only difference is that the solutions show you step by step how they were arrived (sometimes, though, only up to a certain point).

Long and short, you probably won't need this.

5-0 out of 5 stars Good for first Reading
I think Elementary Linear Algebra by Anton is a god bok forlearning the subject. It clearly introduce the subject and it is easily understandable.

2-0 out of 5 stars disapointed
It contains solutions only for selected odd exercises, and most of the solutions are very abbreviated.Despite these setbacks it is still better than no solutions manual. ... Read more

30. Numerical Linear Algebra and Applications, Second Edition
by Biswa Nath Datta
Hardcover: 554 Pages (2010-01-20)
list price: US$79.00 -- used & new: US$79.00
(price subject to change: see help)
Asin: 0898716853
Average Customer Review: 3.5 out of 5 stars
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Editorial Review

Product Description
This second edition of the author s acclaimed textbook covers the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems.

Important features of the original edition have been updated and improved. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB® and MATCOM based. The author also provides a list of key words for quick reference.

The MATLAB toolkit MATCOM contains implementations of the major algorithms associated with the book and enables students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy. Additional online content includes appendices containing MATLAB codes and the MATCOM toolkit solutions to selected problems as well as an extra chapter on special topics.

The topics of generalized and quadratic eigenvalue problems, which arise in practical engineering applications, are described in great detail. This feature, along with an important overview of Krylov subspace methods and an extensively updated bibliography, enhances the book s value as a reference for both engineers and students.

Audience: This book is intended for undergraduate and graduate students in applied and computational mathematics, scientific computing, computer science, financial mathematics, actuarial sciences, and electrical and mechanical engineering. It will also appeal to researchers in mathematics, computer science, physics, chemistry, biology, economics, statistics, and aerospace, electrical, mechanical, and chemical engineering as well as practicing engineers and industrial mathematicians.

Contents: Preface; Chapter 1: Linear Algebra Problems, Their Importance, and Computational Difficulties; Chapter 2: A Review of Some Required Concepts from Core Linear Algebra; Chapter 3: Floating Point Numbers and Errors in Computations; Chapter 4: Stability of Algorithms and Conditioning of Problems; Chapter 5: Gaussian Elimination and LU Factorization; Chapter 6: Numerical Solutions of Linear Systems; Chapter 7: QR Factorization, Singular Value Decomposition, and Projections; Chapter 8: Least-Squares Solutions to Linear Systems; Chapter 9: Numerical Matrix Eigenvalue Problems; Chapter 10: Numerical Symmetric Eigenvalue Problem and Singular Value Decomposition; Chapter 11: Generalized and Quadratic Eigenvalue Problems; Chapter 12: Iterative Methods for Large and Sparse Problems: An Overview; Chapter 13: Key Terms in Numerical Linear Algebra; Bibliography; Index ... Read more

Customer Reviews (5)

2-0 out of 5 stars Good Idea, Poor Implementation
This book is fairly easy to read and covers the subject in a logical order.However the examples and problems are rife with errors and inconsistent nomenclature--making this a hard book to use as a text.

1-0 out of 5 stars Don't waste your money!
This was the required text for a graduate course I had in numerical linear algebra. The 1st edition of this book has hundreds of errors! I don't know if they corrected them in this edition. I learned nothing from this book; It is poorly written.

There is far too much emphasis on LU factorization. Not enough information on sparse iterative methods. In most numerical applications you don't have a full matrix, you have a sparse one. I have been able to sucessfully implement sparse iterative solvers from other books. Some of paperbacks by SIAM are pretty good at that.

5-0 out of 5 stars As good if not better than the standard texts out there
This book is pedagocially sound and extremely informative, and offers a welcome alternative to the standards of the field like Trefethen/Bau and Demmel.

5-0 out of 5 stars A very resourceful and readable book on this subject
While there are many books on Numerical Linear Algebra at various levels, Datta's book is very resourceful and carefully prepared for classroom use. The book is very readable and the students would love it. The organization of the topics, the method of presentation, historical background at thebeginning of each chapter, lucid examples, comprehensive and detailedproofs for almost all Theorems, useful MATLAB exercises for almost all thecomputational methods presented in the book make this book very suitablefor classroom adoptation. Datta has given lots of good references (booksand journal articles) at the end of each chapter, which are useful forfurther research on the major topics. It is a very nice and well-writtenbook. The only suggestion that I have is to add more details on KrylovSpace methods and such topics, and make this book suitable for a wideraudience. I recommend this book strongly.

5-0 out of 5 stars excellent adv undergrad text on numerical linear algebra
Great for classroom and self study. One of the few texts to give step by step examples on almost all of its algorithms,which can be carried out on most hand held calculators. An essential step in the learning process. This book makes learning Numerical Linear Algebra as exciting as it really is. ... Read more

31. Linear Algebra (4th Edition)
by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence
Hardcover: 601 Pages (2002-11-21)
list price: US$141.33 -- used & new: US$99.90
(price subject to change: see help)
Asin: 0130084514
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
This top-selling, theorem-proof book presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.Chapter topics cover vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, and canonical forms.For statisticians and engineers. ... Read more

Customer Reviews (35)

5-0 out of 5 stars Crystal clear and fun
First, while this book does include rigorous (eg clear and complete) proofs, I posit that the book is not a dry tombe and not useless to non-maths students. The book includes enticing introductions to the essential use of linear algebra in Fourier series, differential equations, special relativity, and stochastic processes (with a wink to economics).

*Is this book a good way to startlin alg?*
Answer: possibly yes. Only because the first chapters can seem too axiomatic (at least they were to me when I was a first-year undergrad), I might suggest the more welcoming style of Gilbert Strang. But you decide; I'm not sure why some believe "rigorous proofs" are useless and why others believe "motivation" means no complete proofs (cf. other reviews here).

*Why this book?*
The organization of topics and clarity of exposition makes it well worth acquiring (eg online..).For example, the exercises are well-placed and often used in subsequent chapters. I really enjoyed the chapters on singular value decomposition and least-squares. Here, the examples are especially illustrative and the proofs of the principles provide insight into why things work. The "real-world" applications I cite above are also nicely presented intros. There is more to say here, but there are many more reviews...

*How have I used this book*
One instance: when working at a national lab, one of my projects involved fitting data and I used least-squares as a starting point. Wanting to remind myself about the inner-workings of least squares, I returned to this book and it helped me come up with other ideas to concoct a solution to my "real-world" problem. Also, I am currently studying arithmetic geometry and sometimes come back to it for matrix limits as they are used in distribution of eigenvalues (random matrix theory and function fields).

5-0 out of 5 stars Like the Cryptonomicon of Linear Algebra books!
This book is absolutely amazing! It pretty much psychologically broke me down and built me back up again. It is extremely rigorous and dense, and is very effective. I highly appreciate the small size of the book making it easier to carry around and read.
There are a few caveats though:
You must be ready and willing to prove everything, including material in the book. Often, the proofs of theorems will be left for the problems section. But, if you make the effort, this will increase you theoretical math skills ten fold. Also, I love the fact that this book is so insane, and you might not appreciate that. I used it for a first course in Linear Algebra, which is probably not the ideal application. The book itself suggest that it be used for a graduate level course. I am actually kinda sad I got the paperback, because I will keep this book forever. If you are a professor looking at this book, it really is as versatile as it claims to be.

3-0 out of 5 stars Linear Algebra
This linear algebra textbook is a good book. It has a nice look and feel to it. The author is able to convey the material in a straightforward and precise manner. For someone who is new to the topic, it would be helpful if all odd answers to the exercises were printed and not just a select few. The solutions requiring proofs are omitted. This is where students stumble the most.

4-0 out of 5 stars It will do the job...
It's not a great book, but it will do the job. Just make sure you have a good teacher to fill in all the holes. That's another way of saying it's not a great book if you don't know what it's talking about, i.e. if you're learning from it. If you know the stuff, you'll be fine. You'd probably do better with the free linear algebra book offered online. Just do a search for it.

5-0 out of 5 stars Excellent introductory text
Great first book on Linear Algebra. Doesn't bore you to tears with 100+ pages of matrix crunching before getting to something interesting. I particularly enjoyed the order of presentation, and the well-chosen applications. The book is heavily based around learning how to write proofs -- and it does a wonderful job in providing instructive examples for students on how to go about proving linear algebra theorems.

After reading this, I would go to a more in depth book, but you couldn't find a better place to start than Friedberg. ... Read more

32. Advanced Linear Algebra (Graduate Texts in Mathematics)
by Steven Roman
Paperback: 526 Pages (2010-11-02)
list price: US$74.95 -- used & new: US$60.14
(price subject to change: see help)
Asin: 1441924981
Average Customer Review: 5.0 out of 5 stars
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This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

... Read more

Customer Reviews (3)

5-0 out of 5 stars The true "Linear ALGEBRA".
This is linear algebra as rigorous and beautiful as it can be.

The development of the presented concepts is in terms of advanced abstract algebra; particularly
rings and modules. However, no prior knowledge of abstract algebra is required to study the book,
and this is the very element that makes it a masterpiece. Readers unfamiliar though with basic
abstract algebra should expect to progress quite slowly throughout the book, given that they
show devotion and enough faith to let their minds be guided by the author's educating pen.

Diligent study of the book leads to beautiful insights being emerged that are far from trivial. For
this reason, it is highly recommended that the prospective reader possesses a good level of mathematical
maturity and is already familiar to a sufficient degree with linear algebra and matrix analysis, e.g. at
the level of C. Meyer's "Matrix Analysis and Applied Linear Algebra", which is an excellent first study
of the topic.

"Advanced Linear Algebra" is a book that addresses those who love linear algebra (or algebra) and are
serious about mastering the pertaining concepts. The book is invaluable for combining rigor, depth of
exposition, excellent notation and educational character for a topic of immense importance that pervades
almost every aspect of modern quantitative sciences.

5-0 out of 5 stars Outstanding clarity; this is a very well-written book
Mathematics books are often considerably more difficult to read than their authors prepare their audiences to believe; this book is a happy exception.It is written for an audience of readers at a specific place in their studies (ones who know linear algebra but want to take their understanding of it to a deeper level), and it reaches this audience very well.The emphasis of this book is on linear algebra in abstract mathematics; it is less useful for people interested in numerical linear algebra.

As the name suggests, this book requires a fair amount of background.The introductory chapter moves very fast, but is thorough, and exciting to read.The rest of the book presents advanced topics at a more leisurely pace, while still remaining fairly concise.Some difficult concepts, such as the universal property, are introduced several times at several different places in the book, so that someone working through the book will be more familiar with them when it is finally necessary to understand them on a deeper level.

I find the material on modules outstanding; the author explores the analogies between modules and vector spaces, rigorously exploring which analogies hold, and giving examples of cases in which other analogies fail.The presentation of modules in this book differs greatly from that encountered in most abstract algebra texts: while most books focus on modules' similarities to rings and applications in commutative algebra, this text focuses on their similarities to vector spaces and applications to the study linear operators on vector spaces.

One should not be scared by the word "advanced" in the book's title.Although the book covers advanced topics, it is very clear.When proofs are omitted, it is usually because they are very easy for the reader to supply.The exercises are very valuable (some are critical for understanding the material), but they're not diabolically difficult.

I think this book would make an outstanding textbook for an introductory graduate-level course in linear algebra, or perhaps a senior-level undergraduate course for students with a strong background.It is also very well-suited to self-study.A student with prior background in abstract algebra (group theory, ring theory, etc.) will find this book much more manageable than a student who has not covered such material.People wanting a more introductory text might want to look to the book by Axler, or the old classic by Shilov.

5-0 out of 5 stars A real treasure
Linear algebra is crucial to anyone in a mathematical or technical field. To the pure or applied mathematician, it is the bread and butter -- a lot of fundamental theorems (even in quite advanced fields like algebraic geometry) ultimately come down to a calculation using linear algebra.

In any case, this book is brilliant for the moderately advanced student who knows the basics (maybe sketchily) and wants an extremely comprehensive, rigorous, and coherent review and reordering of his or her linear algebra knowledge. I knew most of the topics in this book in a superficial way, but reading it is quite fulfilling because it all comes together at once.

The choice of topics and the angles from which they are presented is extremely strong. The Jordan and Rational Canonical Forms get a full and rigorous treatment. Unlike many linear algebra books, which use some ugly matrix-related kludge in the proofs of the classification theorems, this book does these topics from the algebraic perspective (i.e., as decompositions of modules over principal ideal domains). Inner product spaces are done in their own substantial chunk of the book, where all the essential ideas are developed abstractly and well. Sometimes linear algebra books focus too much on particular examples of inner product spaces or resort to "magical" proofs of important inequalities. This book takes care to build up important lemmas so that big results fall out "naturally". It is by far the best abstract treatment of inner products that I have read (although it should be supplemented by a knowledge of some of the standard examples, which can be found in a typical introductory textbook).

The proofs are the most elegant possible, with no ugliness or nonsense. The notation is a gem, without confusing mixes of superscripts and subscripts and nonstandard choices. The exposition is at just the right level (for me at least) -- the steps in proofs that are left as exercises are all reasonable and straightforward, and all the details that are subtle or interesting are filled in, discussed, and emphasized.

I have been looking for a beautiful book on linear algebra of this sort for a long time, and am delighted to have finally found it.
... Read more

33. Student Solutions Manual for Differential Equations and Linear Algebra
by Henry Edwards
Paperback: 340 Pages (2009-01-07)
list price: US$36.67 -- used & new: US$36.64
(price subject to change: see help)
Asin: 0136054277
Average Customer Review: 2.5 out of 5 stars
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Editorial Review

Product Description

Known for its real-world applications that grab readers' interest, this proven reference offers a full treatment of linear algebra. Discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. Integrates scientific computing environments like Maple, Mathematica, and MATLAB. Extensively rewrites key sections with a fresh qualitative approach. Adds approximately 300 new computer-generated figures. Adds approximately 300 new or revised problems, many with a qualitative emphasis. A comprehensive reference for anyone who needs to improve their linear algebra skills.

... Read more

Customer Reviews (13)

5-0 out of 5 stars A great text
This book might seem a little bit wordy sometimes, but the author has a great ability to explain complex concepts typically presented in an introductory differential equations course (e.g. Numerical Analysis). It also features an OUTSTANDING coverage of different real-word applications using mathematical software such as Maple.

1-0 out of 5 stars Terrible solutions manual, DON'T PURCHASE!
As with most "official" solutions manuals, this one is pretty much junk.It contains "full" solutions to only odd problems, and those "fully" solutions generally skip steps, assume that you've already mastered the concepts (which you obviously haven't at this level), and on occasion, don't even solve problems the way the book recommends.Instead of purchasing a solutions manual for this DiffieEq book, I'd just recommend using Cramster.For free they've got AWESOME solutions to all odds which clearly explain what's going on, and for ten bucks a month they got you covered on all the evens as well.For some reason this site is not as well-known as it should be, but save yourself some money and headaches and check it out before buying crappy solutions manuals.Just Google "Cramster" and you'll be set!!

1-0 out of 5 stars Very skimpy comments
Besides providing solutions to the problems, this manuel has very few comments.The book is OK for answer check, but not good at all for comments on the problems and solutions.

1-0 out of 5 stars This solutions manual is only minimally helpful...
A good student solutions manual will go through all of the steps of a problem, and show how to solve it.This book skips steps and key ideas.It's not a very good solutions manual.The textbook which it is the solutions manual for is not a well done book, as the problem sets consist of problems which differ enough from the examples that they are frustrating even if you work through and understand all of the examples.The subject of the text is 'differential equations', not 'tricky advanced algebra'.Yet in one of the more difficult fundamental sections (section 1.6, substitution methods), several of the problems, including the first problem, require some not obvious algebraic manipulation to set up and solve.This is not reflected in any of the examples, and it is not shown in this solutions guide - they skip this step.

1-0 out of 5 stars Fine explanation, but Bad Quality
The quality of the explanations in the book are fine.You can learn from it.I learned just fine from the book, as a supplement to attending lectures.What I'm not happy about is that I ordered this book new in late August and come December the cover is already coming off.Why?I didn't put any unusual stress on this book.I have had plenty of hard cover books in my life, many of which were used by students for years before I put my hands on it.Sure, some pages were torn on those books, but the cover was always fine.So when I pay for a hard cover book, I want it to last.This will kill my re-sell value.And I would have brought it to the attention of Amazon or Pearson to save them a bad review but I couldn't figure out how to contact either one. ... Read more

34. Elementary Linear Algebra with Applications
by Howard Anton, Chris Rorres
Hardcover: 864 Pages (2005-01-14)
-- used & new: US$36.00
(price subject to change: see help)
Asin: 0471669598
Average Customer Review: 3.5 out of 5 stars
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Editorial Review

Product Description
This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.

  • The applications version features a wide variety of interesting, contemporary applications.
  • Clear, accessible, step-by-step explanations make the material crystal clear.
  • Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.
... Read more

Customer Reviews (5)

3-0 out of 5 stars not the best
This is the textbook I was required to buy; but because of its sloppy content, I was compelled to buy other books. This may be also due to the fact that my professor is inadequate. However, if you are like me and take responsibility for your learning, consider Linear Algebra by Larson. I bought an older edition for almost nothing. It is so much more thorough and clear.

5-0 out of 5 stars Easy to understand and good homework problems
I just used this book in the Spring '09 semester for the first half of Linear Algebra (my school likes to take forever to get through things, consequently, we have Linear Algebra I and II).

The book was easy to read and understand and the homework problems were pretty good (but at times laborious). It also had a lot of good background information and examples of how this type of mathematics is used today in research and industry.

I got a 3.0/4.0 in the course, so I'm pleased. I would recommend this book for your college.

2-0 out of 5 stars Rough Journey.
This is the text I used this previous semester for my Linear Algebra class. I had no linear algebra background before taking this class. That being said, this was one of the roughest classes I've ever got through only because the book kept going against the grain in every way possible. I didn't even begin to understand the entire point of linear algebra until about chapter 7 and 8 when the chapters started going into the general cases, and even now, I know how to "solve" all the problems without even knowing their meaning, which seems totally pointless to me. The selected answers to the problems in the book are in no particular pattern. It's not "all odds" or "all evens"; it's just scattered and it made doing homework a nightmare. I felt like I was back in elementary school while reading this book, because back then all I did was learn "methods" of solving problems without understanding "why". The book almost never discussed the purpose or main idea of the subjects it discussed. The "explanations" it gave would be based off of other vague topics. For example "What is the Eigenvector Problem? Well, the eigenvector problem asks if there is a basis for R^n in a nXn matrix consisting of eigenvectors of said matrix", OK so What's a basis? "A basis a set of vectors for a vector space S is linearly independant and/or set that spans the space S" and the cycle kept hitting me with one definition after another without giving me a big picture or anything. A bit of the book is about "applications" of linear algebra, but doesn't help until you've understood the meat of the book that came beforehand. Also, there were no teachers' solutions manuals available when I took this class, because the distributers have been extremely lax about getting them out (why? who knows). I'm not just saying this book is bad because I was lazy and didn't do well. I worked extremely hard to do "well" in this class. I must have read this book twice through and like I said before, I can solve all the problems but please don't ask me to explain their significance or validate their existence, because I can't. STAY AWAY!

2-0 out of 5 stars Learn-by-rote Linear Algebra (8th edition)
At my university, David Lay's book is used. They experimented with Anton's (this), and now they're back to Lay's Linear Algebra. Insofar as a Linear Algebra is taught relying heavily on matrixes, I can compare this book with 3 other books: David Lay's; Terry Lawson's; and the one by Hans Schneider and George Barker (Dover book, very cheap). Anton's Linear Algebra has the least theory of all 4. It results in an even poorer product than his Calculus book. Truth be told, I did not use Anton's book, and neither do I wish to. I've suffered too much of his "style" from Calculus, and I saw enough of his Linear Algebra to want to risk jeopardizing my study effort to delve into his book. I'll stick with my other 3 books, thank you very much If you must know: as to what regards "theoretical bent", the order is: Schneider > Lawson > Lay > Anton. Applications: Schneider < Lawson ~ Lay < Anton, but only because Anton's discussions are a little more extensive (not by a great margin). Applications really seems to be its strong point, spanning more than 100 pages in a single chapter, with many interesting and somewhat detailed discussions on "Real World" (to use a term dear to Computer Science types) applications: ecology, graph theory, computer tomography, etc. (none of which you'll learn from this book, by the way, each is a field of its own). I can't recommend it, except as a curiosity.

5-0 out of 5 stars starts with tangible topics
Anton is now in the 9th edition of this book. Spanning decades of refinement. What you get is a very polished and well written text, that has incorporated feedback from generations of students.

The book starts by describing matrix manipulations and determinants. These are very tangible things to most maths students. Accordingly, explaining how to take determinants or to invert a matrix lets you build confidence in your knowledge. Also, these topics lends themselves readily to many problems for you to do.

After this, the book heads into more abstract territory. Null and range spaces and the rank nullity theorem, for example. You are exposed to the concept of an abstract vector space. Which invariably some students always trip over. So the grounding in the early chapters can mitigate this awkwardness.

The last chapter touches lightly on the interesting applications, like chaos and fractals. But mostly to pique your interest in proceeding further in the field. ... Read more

35. Advanced Linear Algebra for Engineers with MATLAB
by Sohail A. Dianat, Eli Saber
Hardcover: 346 Pages (2009-02-23)
list price: US$99.95 -- used & new: US$76.56
(price subject to change: see help)
Asin: 1420095234
Average Customer Review: 4.0 out of 5 stars
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Product Description

Designed to elevate the analytical and problem-solving skills of engineering students, this text provides systematic instruction that will allow those students to make full use of the advanced capacities that MATLAB® provides. Based on the applied experience of two leading industry consultants in signal and image processing and circuit analysis, this textbook is designed to support the highly regarded courses the two teach at RIT. Offering a broad selection of progressive exercises and MATLAB problems, each chapter features carefully chosen examples that demonstrate underlying ideas at work in practical scenarios. A complete solutions manual is provided for qualifying instructors.

... Read more

Customer Reviews (1)

4-0 out of 5 stars Good Book for a Complex Subject
I got this tome as my textbook for a graduate-level Mechanical Engineering course. I entered grad school last fall after about 35 years in the workforce, so I am far more sensitive to the quality of textbooks than I was in my youth.
Anyhow, I have been through the first chapter of Advanced Linear Algebra in detail and have scanned the other five. On the whole, I find that the text does a very good job of explaining matrixes, vectors, and such and their use in engineering.
It is written from an engineering perspective rather than that of a mathmetician, which is a very good thing for us engineering students. Math majors, sickos that they are, will prefer something much more obtuse. The examples used seemto be slanted toward the Electrical Engineering discipline, so they are of less use to me.
All in all, a good textbook. ... Read more

36. The Linear Algebra a Beginning Graduate Student Ought to Know (Texts in the Mathematical Sciences)
by Jonathan Samuel Golan
Paperback: 436 Pages (2007-01-19)
list price: US$109.00 -- used & new: US$75.88
(price subject to change: see help)
Asin: 1402054947
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

Product Description

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. Unfortunately, in recent years the content of the linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate linear algebra course is insufficient for graduate study. This book is intended to fill this gap by providing enough material "theoretical and computational" to allow the student to work independently or in advanced courses.

The book is intended to be used in one of several possible ways:

(1) as a self-study guide ;

(2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level ; or

(3) as a reference book.

It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams.

The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication on the part of the reader. The book also contains over 1000 exercises, many of which are very challenging.

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Customer Reviews (2)

5-0 out of 5 stars Outstanding

This is an excellent introduction to graduate-level linear algebra, touching on theory, applications, and algorithms. It's one of those books I wish had been available when I was in grad school.

5-0 out of 5 stars wonderful for prelims
This book is absolutely terrific for preparing for prelims.The best of its kind available. ... Read more

37. Student Solution Manual for Linear Algebra
by John B. Fraleigh
Paperback: 456 Pages (1995-02-10)
list price: US$36.67 -- used & new: US$21.82
(price subject to change: see help)
Asin: 0201526778
Average Customer Review: 3.0 out of 5 stars
Canada | United Kingdom | Germany | France | Japan
Editorial Review

Product Description
Contains the complete solutions, including proofs, for every third problem in each exercise set. ... Read more

Customer Reviews (16)

4-0 out of 5 stars Linear Algebra
This book was in fairly good condition when it arrived.It was fairly quick as well.

5-0 out of 5 stars excellent!
pretty fast shipping and the book was in great condition!
(the mailman shoved it into my mailbox though...)

5-0 out of 5 stars FAST FAST FAST!!
It came EXTREMELY fast. I am very happy with my purchase. It was a used book and the description was true to the word. I will definitely buy from this seller again. Thanks a lot!

5-0 out of 5 stars Great book.
Taking Linear Algebra for the first time and using this textbook.

I found reading each section and looking at the examples extremely helpful.It was clear and concise.After going through the section, the homework problems presented were a breeze.I think it's a great book to learn from.

3-0 out of 5 stars A Fair Treatment
The book presents linear algebra problems pretty much in outline form---an "ok" treatment for some, but not all, of the subject matter.Nevertheless, there are still many topic areas where the explanations are not thorough enough.
Also,its treatment of theorems is not accompanied by a step-by-step explanaton of a problem that relates to it.
After all, this book is supposed to be an aid for students taking this subject for the first time.

I have found a few editing type errors--in some problems: wrong signs, numbers misplaced.This seems to be an omnipresent problem with many of these type books.WHO IS OUT THERE DOING THE FINAL REVIEWS?

I think this subject matter needs some type of video teaching component, but good luck trying to find one.

I think the book has its advantages, but mainly to those already immersed in the subject matter of matrices and determinants, vectors and space. A didactic tool it is not!
... Read more

38. Elementary Linear Algebra
by Howard Anton
Hardcover: 592 Pages (2010-03-15)
-- used & new: US$102.06
(price subject to change: see help)
Asin: 0470458216
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning. ... Read more

Customer Reviews (13)

5-0 out of 5 stars Shipped Quick
Book came in condition it was said, Brand New. I would definitely recommend Amazon as a seller.

1-0 out of 5 stars Book is a Rip Off
This book from amazon is a rip off. It didn't come with the codes to access the online content which cost like 65 dollars more.Considering it is already almost 120, and it is only like 30 more dollars to buy it from the books store and then you get the codes, it is a rip off.It should state it doesn't come with the codes for online content.All the new books are suppose to otherwise what is the point in buying it new.

5-0 out of 5 stars Execllent Easy to Read
The examples in this book are great.All concepts in the text are explained clearly with many examples for the reader to review.I consider this text to be one of the best that I have used.This text is not only a great text to be used in the classroom, but it is so easy to understand that I also recommend this text for individual learning.

3-0 out of 5 stars Okay if required, but
The Anton book appears to be the standard in teaching undergrad LA, but I personally didn't like it very much. Part of the problem is due to several misprints in the early chapters. Some of the definitions of basic concepts are confusing at best, wrong at the worst. I found myself relying on the Hubbard-Hubbard "Vector Calculus, Linear Algebra, and Differential Forms" to get through the course. The explanations were more concise and easier to understand. If you're teaching yourself, Hubbard-Hubbard is the way to go.

3-0 out of 5 stars Okay if required, but
The Anton book appears to be the standard in teaching undergrad LA, but I personally didn't like it very much. Part of the problem is due to several misprints in the early chapters. Some of the definitions of basic concepts are confusing at best, wrong at the worst. I found myself relying on the Hubbard-Hubbard "Vector Calculus, Linear Algebra, and Differential Forms" to get through the course. The explanations were more concise and easier to understand. If you'r eteaching yourself, Hubbard-Hubbard is the way to go. ... Read more

39. Elementary Linear Algebra
by Howard Anton
Hardcover: 624 Pages (2004-12-27)
-- used & new: US$54.95
(price subject to change: see help)
Asin: 0471669601
Average Customer Review: 2.5 out of 5 stars
Canada | United Kingdom | Germany | France | Japan
Editorial Review

Product Description
This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.

  • Clear, accessible, step-by-step explanations make the material crystal clear.
  • The authors spotlight the relationships between concepts to give a unified and complete picture.
  • Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.
... Read more

Customer Reviews (14)

4-0 out of 5 stars satisfied
Book was a little more worn than expected. Delivery was very prompt. Satisfied with purchase; would buy again.

5-0 out of 5 stars Good over all
This book was very new and had no problems.It was a great book and shipment was fast.

1-0 out of 5 stars Do not even open it
This is the worst LA book I have ever seen.
I would not imagine why any instructor would choose it as a text for the class unless he is paid for it.
Horrible book with horrible exercises (just pile of pencil pushers with no thinking involved).

2-0 out of 5 stars bad book
i'm an engineering major and this is the worst textbook i have used for any math/science class

2-0 out of 5 stars Book causes unneeded frustration
I am currently taking an Elementary Linear Algebra class for college and this book is beyond frustrating. The book barely covers any basics and examples are few and useless. The exercise sets provided are beyond the text and examples provided in the book. Even after purchasing a solution manual, the problems make little sense. Similar to another reviewer of this book, I have resorted to online discussion boards and youtube videos to compliment the lectures from class. ... Read more

40. Linear Algebra (Undergraduate Texts in Mathematics)
by Serge Lang
Paperback: 296 Pages (2010-11-02)
list price: US$64.95 -- used & new: US$52.25
(price subject to change: see help)
Asin: 1441930817
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description

This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.

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Customer Reviews (7)

5-0 out of 5 stars Strong concise book for linear algebra over the Complex numbers
Lang's Linear Algebra is one of my favorite undergraduate math books.The style is concise and clear, and the approach is rather rigorous. I found the chapters on polynomials particularly interesting.

Minor complaints: (1) I would rather Lang have done the book over general (e.g. finite) fields rather than sticking with subfields of the complex numbers.That way it would be more clear which results truly rely on results in Complex analysis and which rely only on the fact that the every n-degree polynomial over the complex numbers has n roots. (2) A couple more examples involving function vector spaces would have been interesting. Although all-in-all he strikes a great balance for as short a book as this is.

4-0 out of 5 stars Difficult for undergrads
I think the term "undergraduate" is a bit misleading.I think you would have had to have at least one course in linear algebra and abtract algebra to truly appreciate this book.I read it over a summer (as a master's student who lacked any coursework in linear algebra) - kind of as an independent project, and I found it to be very easy to understand.Then again, I had just taken abstract algebra.There were a couple parts that I found challenging though.I love it when he says that the proof or rest of the proof is "trivial" and unnecessary to write.I have heard he does this in many of his books.Overall great book if you have some background.

5-0 out of 5 stars Solid piece of work
Like in other math books by Lang, the theory of Linear Algebra is presented in an axiomatic way, the best way of presenting since The Elements of Euclid. The way in which the theory is presented adds to the beauty. I have read this book as a refresher for Linear Algebra, about 20 years after the completion of a master's degree in an exact science. For me the level was perfect. If you have no experience with Linear Algebra beyond high school, you must first read "Introduction to Linear Algebra" by Lang or some other introductory course. The book under review does not talk about basics like Gauss-elimination. I have seen remarkably few typos. Some cross-references to theorems in other chapters were wrong, though. In all: a very good book and well worth the money.

5-0 out of 5 stars Serge Lang is a Very Gifted Expositor
Serge Lang is a very gifted expositor. I've read the reviews saying that his books are notorious for their "dryness". At least as concerns this book - that couldn't be less true.

This book is not only methodical and well written, it is a joy. Every section is a well rounded presentation: Lang clearly and effectively introduces new concepts and patiently develops even the most basic results. But Lang achieves much more: his illuminating examples are stepping stones to a more abstract understanding.

Enjoying this book is like enjoying anything of high quality and craftsmanship. Admittedly, that is not always for everyone to enjoy.

4-0 out of 5 stars This Book Is Almost Excellent
I had this book as the text for my second course in Abstract Algebra, having already taken some elementary Linear Algebra course. I might argue that this is not the best subject for such a course, yet this is very irrelevant here.

All through the class I struggled to understand concepts. I did not. That was not due to the book since I did not even bother opening it. After finishing the course, I realized that the material of this book is of the most importance to anyone planning on continuing his/her grad degree in math, so I decided to read the book. The mission was accomplished in a matter of a couple of weeks.

I do not claim that this is the easiest book to understand the material. In fact, Lang's books are remarked for their dryness. Motivation is almost nonextant. If you, however, have a fairly good background in Linear Algebra (something like the material of Anton's "Elementary Linear Algebra" or the like) and Abstract Algebra (an excellent introduction can be sought in Herstein's "Abstract Algebra") you would much benefit from this book.

The book is a very good book for a second course in linear algebra, that is, it is not a good book for those who had no experience with matrix theory before. The reason is that the book does not mention anything about Gaussian elimination and treats the solutions of n equations in m unknowns using dimension theorems, which is not the standard way of proving existence of such solutions. One more thing is that it does not talk about elementary matrices (one can interpret column or row operations by multiplication of elementary matrices to the right or left). I am not saying the book
is bad, I am saying it is not the right book for a beginner.

The book introduces the basic notions of vector spaces, linear mappings, matrices scalar products, determinants, and eigenvalues and spaces. It then moves to unitary, symmetric, and Hermitian operators and explores their Eigenvalues. Polynomials have a whole chapter followed by triangulation of a linear map. The book concludes with applications of Linear algebra to convex geometry.

I might disagree with the definition of the determinant the author offers, but I would have to admit that his approach is the traditional one.

The subjects of the books must be mastered (or at least absorbed) by anyone who wants to go to analysis (Functional analysis to be precise), Algebra, Geometry, and Differential Equations. To ensure this you should do almost all the exercises of the book since they are so excellent and help a lot in understanding the material presented. ... Read more

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