Linear Algebra and Its Applications (3rd Edition)

Customer Reviews:

Incredibly Accessible.......2007-08-17

I used this book to teach myself linear algebra using a lesson plan developed by a teacher. A few things I found really helpful:

Lay constantly admonishes the reader to carefully study the text, by reading and re-reading. He understands that students learning linear algebra are likely to to be embarking on more abstract/advanced mathematics in the future--and he cares enough to teach good study skills as well as math. I've followed his advice, and found that with proper effort, I am able to teach myself.

Many of the questions are conceptual or True/False, which helps me to retain new concepts.

The study guide (sold separately, but very important if you're self-teaching) only includes answers to odd-numbered exercises. However, the answers are nicely detailed.

I especially appreciate that Lay refuses to flat-out offer answers to conceptual and True/False questions. Instead, there are hints and references to page numbers where helpful information can be found. This is important, not only because it (again) helps reinforce good study skills, but it encourages students to really try a problem before giving up and looking up the answer.

The introduction of new concepts is always followed by one or more examples, which helps to link theory to practice. In general, there are many examples that illustrate good problem-solving techniques. Proofs are detailed and well-justified, and there are some simple proofs that are left as problems in the book. These proofs are simple enough to not be terribly daunting to the student who is new to more abstract mathematical ideas.

For the student who would ask, "well what is it good for?" there are plenty of sections dedicated purely to applications of material learned in previous sections.

Detail-oriented methodical learners like myself should benefit from this book.

a good teacher helps..........2007-08-01

covers 75% of the detail and leaves the 25% up to you. it lacks clear explition is vector space secotion (row col vector nul basis etc). it seems like you do the first coumple of sections not understanding what you are getting at but when you get to chapter 6 or so the past stuff finaly makes sense. I found the book hard to understand when it was talking about maping, one to one on too. i suggest a TI-83 or higher and the solutions manual. The book also lacks pictures showing dimention row col nul basis etc.

Choose Another Book.......2007-07-30

The organization and the treatment given to most subjects are well below what one would expect for a Wikipedia entry on each respective topic.

Anyone who uses this book for any kind of self-study is unlikely to get more out of it more than a few examples on multiplying matrices, row reduction, and some poetry about eigen-spaces and vector spaces.

Take a look at ``Linear Algebra Done Right'' by Alxr.

meh............2007-05-14

This was the textbook that my school has been using for its first and second year Linear Algebra courses. I found it somewhat terse. It seems like it could be a great book for someone already familiar with linear algebra or the logic aspect of mathematics; I don't recommend it for anyone who is not very familiar with proofs. Fortunately, it doesn't lack examples of how to solve computation problems and solutions to the odd-numbered problems are provided in the back of the book. Unfortunately, when it comes to the proof problems, instead of just providing the reader with the answer like most other texts, the author will either mention a hint or refer the reader to the study guide (mine came with a disk which has to be installed on a computer), which could be a problem for readers not familiar with how to do proofs. Serving as a somewhat of a mediator between these two extremes are true/false questions which accompany each chapter in each section of the text. While those start out somewhat fun in the beginning, they can also get tiresome and repetive very quickly. The solutions to these, like the proofs, are not provided, but fortunately, all one has to do is read the text carefully in order to determine the appropriate response.

Shameful Plugs for Study Guide.......2006-03-25

Perhaps the most important questions at the end of each section are the true/false questions dealing with the concepts developed in the section. The computational problems are good for learning the algorithms but the true/false questions represent what you need to know.

After working through them and justifying your answers you turn to the back of the book and look for the correct solution but instead you find something like "Check your answers before referring to the study guide." Unfortunately the study guide is sold seperately so many people, including myself, choose not to buy it, nor should we have to. It makes the author seem like he cares more about selling book then teaching students.

I took Linear Algebra as an online course and there it is even more important that the material in the text is learned from the reading, as there is no physical lecture to supplement it. I would be more understanding if the author included just the answers in the text and left the justifications for the study guide, but to plug the study guide instead is just plain irresponsible.

Linear Algebra and Its Applications, Third Updated Edition

Average customer rating:

An outstanding introduction to Linear Algebra
A very good introduction to linear algebra
Good for the basics
High Quality Linear Algebra Text!
An OK book

Linear Algebra and Its Applications, Third Updated Edition
David C. Lay
Manufacturer: Addison Wesley
ProductGroup: Book
Binding: Hardcover

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Accessories:

Supplement: Student Study Guide Update - Linear Algebra and Its Applications Update: In

ASIN: 0321287134

Book Description

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

Customer Reviews:

An outstanding introduction to Linear Algebra.......2007-08-09

This book provides a good companion for an introductory course in Linear Algebra. Mr. Lay's style is very clear, readable, and each concept logically builds on the last. My only concern is that, like another reviewer said there is the occasional gap between the exercises and the examples presented, which may require the assistance of the instructor. 4/5 Stars

A very good introduction to linear algebra.......2007-07-31

The highest quality of a book is the ability to teach yourself from it. Lay's book is very self-teachable because it is written in a non-pretentious, explanatory way, making sure you get the big picture while making sure you can do the little details. It reminds me of Griffiths books in physics.

It is a little proof light, so I can respect that a mathematician who is into analysis might find this book too easy. Problems aren't too hard but aren't too easy for the more conceptual questions.

And I appreciate that the problems are meant to test your ability to understand the material, not do mindless calculations that I know anyone can do. For example, some matrices will just start off already diagonalized for you in later chapters.

This is written from the perspective of a physicist. I thus say to my fellow scientists that this is a great book to gain a good understanding of the linear algebra. If you are an experimentalist who frankly wants to learn only what he needs to in order to get by, THEN THIS BOOK ISN'T FOR YOU. This book develops from scratch everything you need to know for undergraduate physics. Go read a Differential Equations book and learn as you go for the linear algebra. If you're a theorist, this is for you.

Good for the basics.......2007-07-11

I bought this book in June for a Linear Algebra course I will be starting in the fall. I've been looking through it and reading bits and pieces and from what I see I certainly like this guy's style. I've had completely unusable math books before but this is one of the few that I can use without the assistance of a teacher to at least begin to understand the basic concepts involved. Since I'll be taking the course as a high school student and not as a college student this book seems like it will do just fine to introduce concepts, and, from what I hear, the teacher who is taking over this course in the fall is excellent at explaining stuff so students understand it. Maybe after taking the course I'll change my mind, but for now Linear Algebra and Its Applications is one of the better math books I've ever used.

High Quality Linear Algebra Text! .......2007-01-21

This book is much better than what I feel some reviewers are giving it credit for. Perhaps they have had better exposure than I have to other materials for comparison, but I cannot say for sure.

What I can say is that this book, for me, nearly took the place of the instructor that I had for the course. The book is literally that good at explaining concepts to you and providing relevant examples. I'm not sure what some reviewers meant when they found a gap between the examples and the problems at the end of the chapters, but I did not have this problem anywhere that I can recall.

What I like most about this book, compared to most of the math books I've seen in my day (more than enough, I assure you) is the format of the writing and the exposition of the problems. There are clear, clear connections made between visual and mechanical aspects of the problem. When you are working a linear algebra problem from the book, you should have a good idea of visually what it looks like that you're doing, where columns and rows are positioned, what elements from each are multiplying by the other and what the end result should look like before you get there. I don't typically get this vivid connection between the abstract visualization of the problem and the actual mechanics in other books, but this one poured it on consistently and I really enjoyed that.

The writing style is also casual enough that you don't feel as if you're being led through chapter after chapter of rote and repetition. Instead, it feels like you're being led further and further toward your understanding of the subject and you really are learning something new along the way at each step.

Regardless of what others say, I think that if you have the financial means and the interest, you should definitely include this book in your repertoire of linear algebra references. It is a gem, a guide and an indispensable reference for the subject. There is no other linear algebra text like it.

An OK book.......2006-10-04

While its a very readable book I felt at times that the book leaved out some important details about certain topics. For example it gives an example and explains how to prove something yet gives no directions on how to disprove it, problems still require to do it. Another example later in the book is when it explains how to do something, shows an example, then mentions that some problems have multiple solutions but gives no directions on how to approach these kind of problems or how to make sure that you have all the solutions, you're on your own spending hours trying to put everything together.

Average customer rating:

Great book!
Unsurpassed clarity - and this book just got better!
Non Fiction
Excellent book
A solid explanation of linear algebra

Linear Algebra and Its Applications
Gilbert Strang
Manufacturer: Brooks Cole
ProductGroup: Book
Binding: Hardcover

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Student Solutions Manual for Strang's Linear Algebra and Its Applications, 4th
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ASIN: 0030105676

Book Description

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

Customer Reviews:

Great book!.......2007-10-08

I've used the third edition in conjunction with Professor Strang's excellent video lectures on the MIT OCW site. The combination of the two is absolutely superb. If you do the exercises at the end of each section you will learn linear algebra even if you never intended to!

Unsurpassed clarity - and this book just got better!.......2007-09-15

Professor Strang has taught Linear Algebra for many years to legions of one of the United States' top institution. So give him some credit, for starters...
This book is inimitable in its clarity and in how it yields so much insight. I have many books on Linear Algebra and I think this book is worth its weight in gold. I know of no other book that teaches the fundamental subspaces so well.
The book covers standard material in Linear Algebra (and then some) and has a strong matrix-oriented flavor (as opposed to a book giving an algebraic treatment - look for Valenza if you want that).
I don't understand what some of the complaining is about by some reviewers. The book is not abstract enough, not formal enough? No first treatment in Linear Algebra is or should be - that is Linear Algebra 2. Besides, matrices are pervasive in all fields of engineering, physics, applied math and other disciplines and later on the student will advance to even more complex issues (such as numerical linear algebra) and they simply cannot afford not to have seen the standard matrix treatment. In fact, that would be the reason it's so widely taught - because it's so useful. It's no use delving into abstract treatment if one doesn't understand the most basic facts about why it is that you can solve a system of linear equations.
Best of all, his lectures now can be seen on MIT's Open Courseware site.
I have used this book since the second edition. I believe this 4th edition is the best edition yet. Unlike some other books on the market, this new edition is a fully thought-through new edition (Strang has been restructuring his book throughout all editions, ever making this more clear and insightful). Not bloat at all. I wholeheartedly recommend it. In fact, I believe you might get hurt using some other books that are on the market that do a very lousy job on teaching this subject (such as Lay). This book is the gold standard.

Non Fiction.......2007-09-03

A somewhat dry but good text on the subject. An introduction to vector spaces, among other things. I just looked at fishpond and the price for a new hardcover is $300. Is this delivered by a strip-o-gram, or what? Unbelievable.

Anyway, it is good, but no way it is worth that sort of money given the subject and its age.

Excellent book.......2007-05-28

I stumbled across this book a few years ago when I was visiting someone in Pittsburgh. I woke up early, and having nothing else to do, I picked up Prof. Strang's book to read and I could not put it down. I am a mechanical engineer with an aversion towards mathematics - but Prof. Strang's conversation style completely won me over ( I refer to 2nd and 3rd editions of his book). Since then I have purchased three other books authored by him, and I have watched many of his videos on MIT's OCW website, and I have never felt let down.
No author can write a book that will be acceptable to every reader, and I find some of the criticism of his books exceedingly harsh. If you do not know how to multiply matrices, then this is not the book you want to start with, but once you know a little linear algebra, his video lectures and this book will give you a completely new perspective.

A solid explanation of linear algebra.......2007-02-21

First off, this book is not well-suited for students who have never seen a matrix and have not yet mastered the basic calculations of how to multiply and add matrices, or for those who have never seen Gaussian elimination. There are many other textbooks that do nothing but provide you with exercise after exercise of manual computations of inverses and determinants that are better suited to that purpose.

That said, for anyone taking a course in linear algebra who actually wants to know more than the rote mechanics of matrix multiplication and Gaussian elimination, this book provides a succint explanation of what matrices actually represent. And I've held onto the book as a reference now for many years (referring to the 3rd edition).

I came across it as a graduate student studying for doctoral qualifying examinations. Someone suggested that I check out Strang's book from the library as a supplement to my utterly confounding graduate school text. It was a godsend! I pored over Strang's book, doing computations on occasion, and taking copious notes of his thorough explanations of concepts like null space, row space, column space, and eigenvalues. After that, I had no problem passing my qualifying exam in linear algebra!

Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications)

Average customer rating:

dense monograph
An excellent treatise on applied combinatorics.

Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications)
Richard A. Brualdi , and Herbert J. Ryser
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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Book Description

The book deals with the many connections between matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorical properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix and Latin squares. The book ends by considering algebraic characterizations of combinatorical properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jorda Canonical Form.

Customer Reviews:

dense monograph.......2004-08-29

Sadly the authors have opted for a level
of abstraction that obscures many of the
beautiful details. Particularly disappointing
is the last chapter on matrix theory which veers
off into an odd mixture of marginalia which have
almost no applications.

An excellent treatise on applied combinatorics........1999-10-22

This book is an excellent resource for mathematicians, computer scientists, and engineers. The book shows how to use zero-one matrices and stochastic matrices in your work. The text pretty shows a lot of interesting properties different matrices have and how to compute various values associated with graphs from them. The book would be very useful for people interested in Neural Networks, Speech Recognition, Artificial Intelligence. It is mathematics, though and it describes the properties of the matrices and contains many proofs about these properties. Make sure that you have mastered linear algebra and combinatorics before reading this text.

Division Algebras:: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics (Mathematics and Its Applications)

Average customer rating:

I am waiting for Dixon 's Octonians...
Mathematics behind physics

Division Algebras:: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics (Mathematics and Its Applications)
G.M. Dixon
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792328906

Book Description

The four real division algebras (reals, complexes, quaternions and octonions) are the most obvious signposts to a rich and intricate realm of select and beautiful mathematical structures. Using the new tool of adjoint division algebras, with respect to which the division algebras themselves appear in the role of spinor spaces, some of these structures are developed, including parallelizable spheres, exceptional Lie groups, and triality. In the case of triality the use of adjoint octonions greatly simplifies its investigation. Motivating this work, however, is a strong conviction that the design of our physical reality arises from this select mathematical realm. A compelling case for that conviction is presented, a derivation of the standard model of leptons and quarks.
The book will be of particular interest to particle and high energy theorists, and to applied mathematicians.

Customer Reviews:

I am waiting for Dixon 's Octonians..........2007-02-10

I have not yet received my command. P. MERAT

Mathematics behind physics.......1997-09-29

This is an excellent book for those who want to study Hamilton's quaternions, and other algebraic structures, used in modern physics. Dixon believes that octonions and triality of Spin(8) are essential in understanding particle physics. This clear exposition contains many ideas which have gone unnoticed from other researchers. The book is a treasure trove for mathematical physicists. The author also compares the Cayley algebra of octonions to other algebraic systems used in physics: matrices and Clifford algebras, in particular the Dirac algebra.

Banach Algebras and the General Theory of *-Algebras (Encyclopedia of Mathematics and its Applications)

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Banach Algebras and the General Theory of *-Algebras (Encyclopedia of Mathematics and its Applications)
Theodore W. Palmer
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521366372

Book Description

This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.

Handbook of Linear Algebra (Discrete Mathematics and Its Applications)

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Handbook of Linear Algebra (Discrete Mathematics and Its Applications)

Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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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.

Design Theory (Encyclopedia of Mathematics and its Applications)

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Design Theory (Encyclopedia of Mathematics and its Applications)
Thomas Beth , Deiter Jungnickel , and Hanfried Lenz
Manufacturer: Cambridge University Press
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Book Description

This is the first volume of a two-volume text on design theory. Since the first edition, there has been extensive development of the theory. In particular, the growing importance of discrete mathematics to many parts of engineering and science has made designs a useful tool for applications. The authors acknowledge this trend with an additional chapter on applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering. The book features exercises throughout and concludes with an extensive and updated bibliography of over 1800 entries.

Handbook of Categorical Algebra (Encyclopedia of Mathematics and its Applications)

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Handbook of Categorical Algebra (Encyclopedia of Mathematics and its Applications)
Francis Borceux
Manufacturer: Cambridge University Press
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Binding: Hardcover

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Handbook of Categorical Algebra (Encyclopedia of Mathematics and its Applications)

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The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.

Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)

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Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)
Xiaoping Xu
Manufacturer: Springer
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Book Description

This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices.
Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.

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