Product Description
This third edition of the successful outline in linear algebra--which sold more than 400,000 copies in its past two editions--has been thoroughly updated to increase its applicability to the fields in which linear algebra is now essential: computer science, engineering, mathematics, physics, and quantitative analysis. Revised coverage includes new problems relevant to computer science and a revised chapter on linear equations. ... Read more

Customer Reviews (29)

Superficial; only good for the exercises
This book does not really teach Linear Algebra. It's very superficial and not interesting. Try Jim Hefferon's book instead and you will have a clear text that teaches Linear Algebra for real.

Anyway, there are several exercises in the book -- that is one reason to buy it, I think...

Excellent text, but errors galore in the answers to the exercises
I'm using this book to review Linear Algebra, having been away for quite some time. The basic text is easy to follow, and the ideas are clearly explained. But the amount of errors in the answers to the exercises are totally unacceptable. If I was a teacher again (which I was years ago) and a student turned in this quality of work for the exercises, they would get a failing grade. The typos and errors really are that bad. I have found that I do not trust the answers given in the book, as I am using my computer to do the math to double check my practice. I absolutely have to agree with others, the book itself is good, but the answers to the exercises are so bad that I can not recommend this book, which is unfortunate as the explanations of Linear Algebra are actually quite good.

Fourth Edition is out
The Fourth Edition of this book is out.It should have corrected some typos that I saw in this edition.It's priced about the same, so I suggest you get that one instead.See link below.

Schaum's Outline of Linear Algebra, 4ed (Schaum's Outlines)

When asked to recommend a supplemental linear algebra text, this is always the one
Over my career as a college educator, I have occasionally taught linear algebra and have had students ask me if I knew of a resource they could use for additional help and practice. My answer has always been to refer them to this book. Even the most abstract mathematical theory is learned by seeing problems worked through and then doing some of them on your own. As every math teacher knows, mathematics is a participatory sport and participation is defined as being intellectually engaged in following logical reasoning.
The problems in this book start at the very beginning and cover the fundamental principles of linear algebra. If there is a weakness, it is that there is nothing in the way of applications. Linear algebra and matrices forms one of the mathematical foundations of creating moving images via computer and that is one way to quickly pique the interest of the students (and instructors).

Good resource - not up to Schaum Outline standard but good
As others have noted there are simple mistakes - I was suprised at the first few early ones I found (addition mistakes, mixing variables). I almost got another book based on other reviews to supplement my course text (Anton's which is pathetic), but overall the Schaum's Outlines have been very good for me and ultimately this one did have enough examples to be helpful.

Not as helpful as many of the other Schaum Outlines but I'm not terribly disappointed as I feared based on other reviews. ... Read more

Product Description
Prominent Russian mathematician’s concise, well-written exposition considers: n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, introduction to tensors, more. Not designed as an introductory text. 1961 ed.
... Read more

Customer Reviews (7)

Very good textbook for the application-minded person
I can only strongly recommend this somewhat forgotten textbook to anyone who needs a basic but otherwise thorough exposition to linear algebra. It conflates rigor, examples, and exercises very nicely. Its coordinate-oriented presentation may not appeal to the mathematician in search of ultimate generality, but it is ideal for the physics and engineering-minded person. It is unfortunate that nowadays so many S&E students become first aquainted with rings of polynomials than with rotation matrices! Do not get me wrong, though: the book contains real math inside, but in the best Russian textbook presentation tradition.

One of the most complete linear algebra texts
The bilinear (quadratic like) form is related to the inner product in this text: two things that are almost entirely left out in many American linear algebra texts. The text is a translation from Russian and
is somewhat difficultwith the axiomatic development form used.
Explanations, examples and problems aren't a real part of this method of presentation, so the resulting text is more like a graduate text
than the second year texts of American Linear algebra.
The price is right for real students of algebra.

Average to Poor
It's a relatively dry and straightforward presentation that is no more difficult or easy to understand than most other traditional books on LA.The style has an antiquated feel to it, and as such, is rather dense and cold in presentation -- truthfully, extremely boring like reading a list of definitions in a dictionary. Not nearly as clear or engaging as Harvard's Otto Brescher in his undergraduate text "Linear Algebra with Applications", nor as clever as Klaus Janich's "Linear Algebra".

Excellent and Compact book
The professor who recommended this book made the comment that every time you re-read it, you notice something else that you missed the last time you read it.This is absolutely true.

I must say, the first time I picked up this book, I did not like it.The notation was not what I was used to, and the book dives right in, assuming a lot of background (matrices, determinants, etc.) but covering material which many people find boring (bases, etc.).However, when you read deeper, there's a lot here.Once you get past the ugly notation, the proofs are extraordinarily clear.And in spite of the books small size, there is a remarkable amount of motivation and discussion.

Like the other reviewer said, this is not a book to learn linear algebra from for the first time: this is an advanced book that is useful for graduate students who have already had a linear algebra course and who want to learn more topics, or understand topics on a deeper level.

This is an excellent book; the bottom line is that it's so cheap that there's no excuse NOT to buy it.

Best linear algebra book
Lucid and clear notation , complete explanations . This books was first published in
1937 but until now it remains best text book in the field . ... Read more

Customer Reviews (1)

Good book
This book is decent.It demonstrates very easily how to use MATLABto solve systems of equations. ... Read more

Product Description
Undergraduate linear algebra is both beautiful and replete with real world applications and connections to the rest of mathematics. The purpose of the present volume is to enrich the understanding of linear algebra for a wide audience by placing a broad collection of short items in the hands of teachers, students, and others who enjoy the subject. Because undergraduate linear algebra is so fundamental to the mathematics curriculum, it is often taught by non-specialists and specialists alike. "Linear Algebra Gems" offers to all teachers clever ways in which core ideas can be presented to their students.

Most articles are accessible to those with modest preparation in linear algebra, including beginning students. However, many items will also contain pleasant surprises even to those well-versed in the subject. The editors have combed through the literature, and have selected from original submissions, to find expository articles and problems to enrich the reader's understanding. The seventy-three articles selected are organized into nine sections, with over 120 problems grouped into subject categories as a tenth section.

Contributors to the volume include experts in the field and long-time teachers of linear algebra. The book was prepared as part of a broad contract with the National Science Foundation to improve undergraduate linear algebra education. The editors hope that many readers will find enjoyment from this collection. ... Read more

Customer Reviews (1)

If you need some small sparks of new material in your linear algebra classes, this is the book for you
Years ago, I taught the two-semester calculus sequence for several years in succession. While that made it easy and routine for me to present the topics in lecture, I also recognized the potential for becoming stale in focus. It is easy to repeat yourself year after year, after all your audience changes, so there will be no complaints.
In order to avoid this "rusting in place", it is necessary for the teacher to search for and find new, different and interesting ways to present the material. In the area of linear algebra, where the same potential for stagnation exists, this book will solve the problem. It contains sets of very short proofs, applications and operations of the fundamental principles of linear algebra. In most cases, you will not find them in linear algebra books, so they will give you new ways to present the material.
Fortunately, technology is generally not a part of these short bursts. Since the goal is to teach what linear algebra is and what it can be used for, using a symbolic mathematics package would be a hindrance to the understanding. If you teach linear algebra and are looking for some new sparks, this is the place to look.
... Read more

Product Description
This valuable study guide provides a modern introduction to linear algebra for people studying or practicing in any of the varied fields of mathematics, physics, biology, chemistry, economics, statistics and engineering. The hundreds of problems solved step-by-step illustrate and reinforce key points. And 390 additional problems help students review the information in each chapter and consolidate their knowledge. ... Read more

Customer Reviews (6)

It came fast!
I really needed this book fast and appreciated how quickly it arrived. It was in the condition I expected it to be in. I made a good choice.

Good book
This book has been delivered fast and really good book for introductory linear algebra. Lots of problems have been solved and this book is good for quick review of linear algebra also.

Linear Algebra
Anyone who wants to learn linear algebra can do it alone with this book if they have a good grasp of ordinary algebra.I think it should be a prerequisite for any course in differential equations.

OUTSTANDING!
I ordered this book to use along with my text.It made the course much easier tounderstand.This book is the only reason I made a B in linear algebra.I just ordered the other books to use for abstract algebra and probability also. Buy it!

Better and easier than sitting thru a confusing instructor
Want to ace linear algebra and not get confused all the time? This book can help solve even the trickiest problems in linear algebra and helps understand the more complex and complicated concepts of linear algebra. Buy this book and get ahead and never get left out in the cold again ! ... Read more

Product Description
Intended for a serious first course or a second course in linear algebra, this book carries students beyond eigenvalues and eigenvectors to the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices. The authors present the material from a structural point of view: fundamental algebraic properties of the entities involved are emphasized. The approach is particularly important because the mathematical systems encountered in linear algebra furnish a wealth of examples for the structures studied in more advanced courses. By taking a straight and smooth path to the heart of linear algebra, students will be able to make the transition from the intuitive developments of courses at a lower level to the more abstract treatments encountered later. ... Read more

Customer Reviews (4)

Terrible textbook
This is a textbook about linear algebra in my undergraduate study, but this book is worse than any other books with same topic.
Only some example are easy to understand, but most of them are chaotic order, specially in proof of definition. I do not want to use any more.

Do not buy this book if you ever want to grasp linear algebra.
This term, I have the misfortune of using this textbook for a second year linear algebra course.When I paid $150 for a text book, I assumed that there was some sort of rationale for such a high price; as of yet, I have not found one.Not only are the explanations of particular examples muddled at best, the wording of most concepts is completely convoluted.The only way that I am getting through this course is with my laptop open to Wikipedia to help me decipher this.Aside from that, the authors provide "selected examples" which aren't overly helpful, and often are completely erroneous.The book could also be improved by a glossary and chapter summaries.

Just awful!
I had the doubtful pleasure of teaching a 2nd year linear algebra course from this text at a major Canadian university recently. This is an awful textbook. The proofs are muddled and poorly presented, so much so that it makes you wonder if the authors know what they're talking about. But what makes this text so bad is that the examples are so poor, like it was some last minute addition, an afterthought. If the authors had found some interesting examples, or even applications, and worked them out clearly, I could have forgiven that the proofs are poorly written, but no. There are many better texts out there that do a better job, and some are even available online for free. So stay away from this one!

A book not worth to study lin algebra by
This is one of the most stupid books on linear algebra i have ever seen. The explanation of theory is awful, examples given do not provide a student with any idea of what is going on. The solutions of the examples are shortened so that it is very hard for a student to understand all the procedures and the logic behind the solution. ... Read more

Product Description
A comprehensive review guide to help you refresh your study. This guide is particularly useful for midterms and final exams, condensing a semester's worth of information into one concise volume. ... Read more

Customer Reviews (4)

Watered down linear algebra
It won't help you pass a college Linear Algebra course.
At least it didn't help me.
Problem is that it's just too small to really go into any depth so all it's good for is if you need help memorizing the formulas for the determinant, eigenvalue,etc.
If you don't understand the concepts behind all the formulas this book won't help at all!
Then again I guess that's all it aims to do.
Also some of the notation may vary from what you see in other linear algebra books.

Excellent and reasonably comprehensive introduction to basic linear algebra for the self-motivated student.
This book is an excellent introduction or review of linear algebra.It presents the most important aspects of basic linear algebra quickly, concisely, and accurately.It begins with concepts from vector and matrix algebra and continues through 318 pages to end with Eigenvalues and Eigenvectors. It presents a concept, e.g., linear independence, and then provides at least one example illustrating the concept.After a short discussion of each new concept, a fully-worked example is provided. Pages frequently appear with multiple examples.

There are no exercises with answers for the student to check their comprehension. You can instead use the examples as exercises, which works quite well since the examples are fully worked out. However, you must bring your own motivation to this Quick Review.Although the work is over 300 pages it presents "just the facts" and spends essentially no time building motivation or interest. Highly recommended, but only for the self-motivatedreader.

Digital Editions are a nightmare!
The book itself is excelent.Digital editions are a nightmare!I had t wipe out my computer due to a virus.Amazon doesn't let me download it again and there is a cumbersome procedure to reactivate the book through acrobat reader.After you do it, it still doesn't work.Customer service at Yahoo for this sucks too!So, if you value your time and your money, get only hardcopies!!!!!!

get it!
this book is an excellent addition to or replacement for your college text. i was even able to stop attending class. thanks! ... Read more

Product Description
Using a dual presentation that is rigorous and comprehensive—yet exceptionaly reader-friendly in approach—this book covers most of the standard topics in multivariate calculus and an introduction to linear algebra. It focuses in underlying ideas, integrates theory and applications, offers a host of learning aids, features coverage of differential forms, and emphasizes numerical methods that highlight modern applications of mathematics.The revised and expanded content of this edition includes new discussions of functions; complex numbers; closure, interior, and boundary; orientation; forms restricted to vector spaces; expanded discussions of subsets and subspaces of R^n; probability, change of basis matrix; and more.For individuals interested in the fields of mathematics, engineering, and science—and looking for a unified approach and better understanding of vector calculus, linear algebra, and differential forms. ... Read more

Customer Reviews (18)

Overpriced
Be sure to buy the third edition. But don't pay $100. The web site price at one of the two major book store chains is $63 plus shipping. The other chain does not sell it. Or buy it used for $25 to $40.It is a difficult book. Expect frustration with an author so vain he makes up his own notation. The Student Solution manual (ISBN 9780971576643) for the third edition is an extra $33 and gives methods for solving odd numbered problems. It is a necessity. The solutions manual makes up for some of the text book's opacity. Currently Amazon does not sell the solutions manual. The only place I've found the student solutions manual is at matrixeditions.com.

Excellent approach to vectors, forms and things linear and integrable
Lots of people know vectors, even today a lots less know forms. This is a real shame because forms are simple and elementary, yet there are very few sources that introduce forms on a concrete level. The authors introduce the concepts of vectors, integration, and forms on a level that is accessible to a bright and interested high-school student.

Traditionally calculus in higher dimensions taught at an introductory level uses a vectors-only approach. This leads to considerable extra effort to account for two basic things: One is orientation, the second is how to generate higher-dimensional objects from lower-dimensional ones while keeping the same operations intact. For example how can one compute the length of a line, the area of a parallelogram or the volume of a parallelepiped (and higher dimensional version of this) in a linear context?

The answer to this are forms, and if they arise in a differential setting, differential forms. The alternating product (outer product) that calculations with forms bring automatically encode the important property of orientation. At the same time they describe what "area" would be in any dimensions, and if one takes infinitesimal versions of these how to integrate them together to areas of differentiable manifolds.

This book does all this right. It introduces forms in a straight forward way, gives pictures that shows how they look, gives geometric interpretations of computations (like the simple, yet all too rarely taught fact that the determinant of a square matrix is the volume of the vectors making up the matrix). Readers with this knowledge will suddenly have a deep understanding why one gets a determinant when one changes variables in integration!

For anybody who wants to have a good foundation for differential geometry, have a better understanding of vector calculus than most other/older text on the topic contain, or just wanted to know what those forms really are that geometers in more advanced texts just define algebraically, this is at present the best text I know to learn this.

There are other texts (though not too many) that attempt at giving elementary treatments of vector calculus and forms. For example William Burke's "Applied Differential Geometry" is one such text, which also contains graphical representation of forms. By taking a more computational approach the present text does, I think a better job, in clarifying forms in application. Another text would be for example Harvey Flanders' "Differential Forms with Applications to the Physical Sciences". This is a considerably more advanced text than Hubbard's and lacks many elementary foundations and basic geometric properties that Hubbard lays out quite nicely. People interested in electromagnetical applications but also just lots of visual ways of representing forms should check notes of Selfridge, Arnold and Warnick.

I have just two minor remarks. The book is filled with interesting short bios of relevant mathematicians, yet Hermann Grassmann who is primarily responsible (and chronically undercredited) for the introduction of forms is not mentioned in the text.

The second is that I disagree with Hubbard's stance (citing Dieudonne) that multivalued function are meaningless. There are in fact problems that look simpler when multivalued functions are allowed and there are ways to compute with them (branch cuts etc).

But these are minor comments that don't take anything away from this being a great text.

In all this is a beautifully written text on vector calculus, integration and differential forms that I can highly recommend to undergrads yet also graduate students and working colleagues.

I really hope that texts like these will soon be typical for introductory courses on vector calculus and integration, because this is essentially how it should be done... it should be easy to see why after reading the text.

Mathematically sound without being too difficult
This is one of the best math textbooks you'll ever find--it stresses the computational aspects of multivariable calculus and linear algebra without losing sight on the mathematical theory. Hubbard presents material that most math students wouldn't otherwise touch until analysis in a down-to-earth fashion.

The unified approach of this textbook is particularly enlightening. I am convinced that vector calculus must absolutely be taught with differential forms--there is no other way. While Hubbard's notation is clunky and unorthodox at times, compare the traditional notation of Stokes' Theorem to Hubbard's, and you will appreciate the elegance.

Good generalization of Calculus for motivated students
This book provides a good grounding in the essential topics needed to use calculus effectively.As other readers here have mentioned, the Hubbards' book presents a wide range of mathematical concepts that are very useful to develop mathematical thinking.Moreover, the material is presented in a basic level so that students just coming out of high school can easily pick up the material.Indeed, after taking one year of single variable calculus I used this book in my undergraduate class that was title "Honors Mathematics".Without it, and using the typical Stewart Multivariable book, I would have had much more difficulty adapting to the abstractness in my next year with Analysis, Algebra, and Topology.

There are some difficulties with the notation and typos, but none that can be overcome with some thought.The material is presented in such an orderly and integrated fashion that is hard not to learn from the book, regardless of your mathematical level as long as you fulfill the prerequisites (single variable calculus) and work to understand the material right off the bat.

A Pleasure to Read
First of let me state that I own the 2nd edition of this book, and that I am a doctoral student in computational physics.

After borrowing this book from the library, I read it cover to cover.I then bought a copy for myself to use as a reference.I learned a lot about the foundations of mathematics that I had not learned as a physics student.The book is very clearly written and actually enjoyable to read, with many examples, applications, and historical notes.The proofs were easy for me to follow.

Although the book is mainly concerned with multivariate calculus and linear algebra, it touches on many interesting and important matehmatical topics from set theory, topology, differential geometry, fractals, chaos, and analysis.It also provides an appendix that gives proofs for 25 of theorems that are considered harder to prove than is expected for a text of this level.

I also appreciated that the notation is thoroughly modern. (A glossary to the notation is given on the inside cover, with references to where in the book that you can find the full definition and explanation.)This may well be a drawback for many people, but for me it was very helpful because I now have an easier time reading papers on the more mathematical side of physics.Another modern aspect of this text is the introduction of differential forms, which are becoming essential to theoreticians in many branches of physics (quantum field theory, string theory, classical mechanics, and general relativity).

Lastly, this is a book on "pure mathematics", so if you are only interested in applied math, you will not like this book.

For me, it's been a great investment! ... Read more

Product Description
This revision of a well-known text includes more sophisticated mathematical material. A new section on applications provides an introduction to the modern treatment of calculus of several variables, and the concept of duality receives expanded coverage. Notations have been changed to correspond to more current usage. ... Read more

Product Description

Product Description
The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research.

The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts.

Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems. ... Read more

Product Description
Practical Linear Algebra introduces students in math, science, engineering, and computer science to Linear Algebra from an intuitive and geometric viewpoint, creating a level of understanding that goes far beyond mere matrix manipulations. Practical aspects, such as computer graphics topics and numerical strategies, are covered throughout, and thus students can build a "Geometry Toolbox," based on a geometric understanding of the key concepts.

This book covers all the standard linear algebra material for a first-year course; the authors teach by motivation, illustration, and example rather than by using a theorem/proof style.

Special Features:

Product Description
This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject. ... Read more

Customer Reviews (6)

A valuable source
This book (the original version) has all the basics to introduce the future differential equations/dynamical systems researchers into the field. Written by authorities in the field (Hirsch and Smale,) this text offers a wide variety of topics, including linear systems, local and global stability theory for non-linear systems, and applications to physics and biology. As an added treat, the inclusion of basic linear algebra and operator theory makes this a rather self-contained work. The dedicated reader will not be disappointed - the material is well organised with sufficient level of detail, illustration, and exercises.

This is not a recipe book
I can see that this is not the book for you if you want to solve a particular differential equation.But in terms of understanding the field of dynamical systems, there is no rival.This book is a pleasure to read, for the first time I understood the importance and beauty of linear algebra.Academic Press says that this is their most successful mathematics text, and it is not hard to see why.I wish more texts were as clearly written and as beautiful to read.

A complete waste
This is not a book, it's a piece of trash!!! This so called book is a meaningless mess which wasn't even understandable for the person who had a PhD in math and was teaching our class. Do NOT bother with this nonsense. if you want to learn something just read Ordinary Differential Equations by V. I. Arnold.I would have given no star if I could!!!Just go with Arnold's and I'll be WAY better off.

Not for the average undergrad!
As a senior undergrad majoring in math and economics, this book is everything but an easy read. To all fellow undergrads who are not math superheroes (that should about 75% of us), if you happen to come across this book in an upcoming course description, it may be a good idea to look for alternative. Currently, I'm looking for another book that I may be able to use as a supplement to get me through this course with a passing grade. Up to this point in my math career, I have never come across a text as ungraspable as this one; this is unfortunate since it appears that there is a lot of knowledge and content on the pages.

Thorough and solid introduction
This is the book from which I was introduced to dynamical systems some twenty-odd years ago. It's a thorough introduction that presumes a basic knowledge of multivariate differential calculus but is pretty well self-contained as far as linear algebra is concerned. Rigorous but readable, it provides a foundational understanding of n-dimensional linear dynamical systems and their basic exponential solution.

But my opinions won't be as helpful to the Amazon math shopper as a simple listing of what's in the book. So here's the table of contents.

Chapter 1: First Examples

Chapter 2: Newton's Equation and Kepler's Law

Chapter 3: Linear Systems with Constant Coefficiants and Real Eigenvalues

Chapter 4: Linear Systems with Constant Coefficients and Complex Eigenvalues

Chapter 5: Linear Systems and Exponentials of Operators

Chapter 6: Linear Systems and Canonical Forms of Operators

Chapter 7: Contractions and Generic Properties of Operators

Chapter 8: Fundamental Theory

Chapter 9: Stability of Equilibria

Chapter 10: Differential Equations for Electric Circuits

Chapter 11: The Poincare-Bendixson Theorem

Chapter 12: Ecology

Chapter 13: Periodic Attractors

Chapter 14: Classical Mechanics

Chapter 15: Nonautonomous Equations and Differentiability of Flows

Chapter 16: Perturbation Theory and Structural Stability

Afterword

Appendix I: Elementary Facts

Appendix II: Polynomials

Appendix III: On Canonical Forms

Appendix IV: The Inverse Function Theorem

References

Answers to Selected Problems ... Read more

Product Description
Rigorous, self-contained introduction at undergraduate level covers vector spaces and linear transformations, linear equations and determinants, characteristic roots. Includes 16 sets of true-false quizzes and exercises (with worked-out solutions), a complete theory of permutations and much more.
... Read more

Customer Reviews (1)

Pleasure to read
It is a pleasure to read the book. There is a quiz and a set of exercises at the end of each section. Contains solutions to all quizzes and exercises; most suitable for self study. Table of contents:

Preface
Chapter 1: Vector Spaces and Linear Transformations
1. Vector Spaces
2. Linear transformations
3. Inner product
4. Matrix representations
5. Inverses
Chapter 2: Linear Equations and Determinants
1. Rank of a matrix
2. Operations on matrices
3. Linear equations
4. Permutations
5. Introduction to determinants
6. Properties of determinants
Chapter 3: Characteristic Roots
1. Characteristic roots and characteristic vectors
2. Schur's theorem
3. Normal matrices
4. Hermitian matrices
5. Matrix inequalities
Answers and Solutions
Index ... Read more

Product Description
Never HIGHLIGHT a Book Again!Virtually all testable terms, concepts, persons, places, and events are included. Cram101 Textbook Outlines gives all of the outlines, highlights, notes for your textbook with optional online practice tests. Only Cram101 Out ... Read more

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Covering both theory and progressive experiments, Quantum Computing: From Linear Algebra to Physical Realizations explains how and why superposition and entanglement provide the enormous computational power in quantum computing. This self-contained, classroom-tested book is divided into two sections, with the first devoted to the theoretical aspects of quantum computing and the second focused on several candidates of a working quantum computer, evaluating them according to the DiVincenzo criteria.

Topics in Part I

• Linear algebra
• Principles of quantum mechanics
• Qubit and the first application of quantum information processing—quantum key distribution
• Quantum gates
• Simple yet elucidating examples of quantum algorithms
• Quantum circuits that implement integral transforms
• Practical quantum algorithms, including Grover’s database search algorithm and Shor’s factorization algorithm
• The disturbing issue of decoherence
• Important examples of quantum error-correcting codes (QECC)

Topics in Part II

• DiVincenzo criteria, which are the standards a physical system must satisfy to be a candidate as a working quantum computer
• Liquid state NMR, one of the well-understood physical systems
• Ionic and atomic qubits
• Several types of Josephson junction qubits
• The quantum dots realization of qubits

Looking at the ways in which quantum computing can become reality, this book delves into enough theoretical background and experimental research to support a thorough understanding of this promising field.

Customer Reviews (1)

Quantum Computing: From Linear Algebra to Physical Realizations
This is a wonderful textbook and reference book.
Good for self-study and instruction.
... Read more

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Customer Reviews (1)

But you must take it for what it is.
This is not a standard linear algebra text. If you're looking for an introductory book or even a geometrical-themed supplement to an introductory book, this is NOT what you are looking for. Baer assumes you have already mastered standard linear algebra, and are quite familar with fields, groups, rings, isomorphisms, homomorphisms, Galois theory, etc. He also assumes you have a grasp of the concepts and theorems of projective (and some affine) geometry. There are no explicit exercises or problems, but more than a few non-trivial statements/theorems and non-obvious facts are left for the reader to prove or justify. The table of contents can be found at:
http://web.doverpublications.com/cgi-bin/toc.pl/0486445658

This book is a good follow-up to _Linear Algebra: A Geometric Approach_ by Sernesi (Chapman & Hall), which is "introductory" (although not really for the rank beginner) and mostly focuses on affine geometry. If you're looking for a geometric supplement for an introductory course, try _A Vector Space Approach to Geometry_ by Hausner (Dover).

With those caveats out of the way, this is great book, even if upon first reading some sections are so dense that they bend light. But as you work through it, there are many moments of illumination if you have a bent for the interplay and fundamental equivalence between algebra and geometry. But it isn't spoon-fed to you.
... Read more

Product Description
This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53) ... Read more

Product Description
The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metric, the theory of Hilbert polynomials, and projective and affine geometries. This comprehensive volume is unusual in its extensive use of applications in physics to clarify each topic.
This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from most existing textbooks in approach, the work illustrates the various applications and connections of linear algebra with functional analysis, quantum mechanics, and algebraic and differential geometry. ... Read more

Customer Reviews (1)

an ordinary book about linear algebra
this is an elementry book about linear algebra and a reviewer who receive a first coarse in linear algebra will find it an excellent book but it is an elementry book! ... Read more