Reviews (4)

PhD Student
This book is really just an introduction to NLA and intended for the novice although it assumes some LA background.It is not necessary to read this if you plan PhD studies in the field since the book is only an introduction to the material and is honestly too simple.Read anything by Bjorck or Van Loan if you are a serious PhD student and want to do research in the field of NLA.This book is written for students that really don't plan research in the field of NLA but rather may need some skill level in NLA to perform their job or their own own research which may have some NLA exposure.

This book grows on you
I used this text for a two-semester graduate sequence in numerical linear algebra (NLA) while I was a graduate student in the Mathematics Department at The University of Kentucky.If you do not have a substantial background in linear algebra and numerical analysis, which I did not when I first used this book, the material covered and the presentation can seem to be quite daunting.But while the presentation is very thorough, it is not unnecessarily so.After I had used this text for about three months, I grew accustomed to the very detailed nature of the writing and grateful for the sheer level of information contained in a meer 419 pages.

Many introductury numerical analysis books include several chapters covering the commonly used algorithms in NLA but usually not in complete detail.While this format is friendlier to use for an overview of the "basics," in the real world, the standard ways of solving numerical systems such as GEPP, SVD, QR, Cholesky decompostions, Gauss-Siedel iterations, and other methods do not always work in a nice cookbook-like fashion.When one of these standard methods that engineers and research scientists use to solve "standard" problems fails, and it will sometimes, this book will give you a good starting point to figure out what went wrong and what alternate methods can be used to solve a linear system that is not as easy as it first appeared to be.

If you are learning NLA, you are probably doing so because you either want to or have to apply it in your professional life, by which I mean your job or the job that you hope to get.In my current position, I develop and design statistical and deterministic simulators for human genetics research.And when I need to used Cholesky decompostions, SVD's, and other NLA methods, I always consult this book to review how these methods work and, more importantly, what innocent looking data will cause these methods to fail silently - in other words, give results that look reasonable, but are completely wrong.In conclusion, this book is not the easiest to read.But it is one of the best resources available when you need to learn how to handle basic and not-so-basic problems in the field of NLA.

Reviews (5)

Not for the uninitiated
I bought this book hoping to learn about matrix analyis. I did not. Thisbook is simply a reference manual with plenty of theorems, axioms etc. withlittle explanation. They give it to you rough and row. NOT A SINGLE SOLVEDEXAMPLE, and not evensolutions for the exercises given in the book areprovided. If you intend to learn about matrix analysis, as I did, let notthe 5 stars review mislead you. Don't make the same mistake, this book isnot for you.

An encyclopedic reference for matrix analysis and linear alg
Horn and Johnson's MATRIX ANALYSIS is simply a masterpiece. You can findeach and every result in matrix analysis along with it's proof in thisbook. Look at their companion volume "Topics in Matrix Analysis"too. Some of these results cannot be found elsewhere.

Excellent book.... for the initiated
Horn and Johnson has written an excellent reference book onsomewhat-advanced linear algebra (from the point of view of an engineer).There's a lot of treasures in this book, but this book is NOT for beginninglinear algebra. Rather, it is written as a handy reference to review andlearn certain topics in linear algebra.

Nonetheless, I really like theirtake on linear algebra. They motivate you in every subject and problem (forexample, the relations between eigenvectors, eigenvalues, and optimizationproblems). These insights are invaluable and definitely worth the admissionprice.

Reviews (13)

One of the best books on the subject
This is the book I turn to first when I have to deal with a problem in numerical linear algebra, it's clearly written and has extensive references.

Got Matrices?
This is one of the definitive texts on computational linear algebra, or more specifically, on matrix computations.The term "matrix computations" is actually the more apt name because the book focuses on computational issues involving matrices,the currency of linear algebra, rather than on linear algebra in the abstract. As an example of this distinction, the authors develop both "saxpy" (scalar "a" times vector "x" plus vector "y") based algorithms and "gaxpy" (generalized saxpy, where "a" is a matrix) based algorithms, which are organized to exploit very efficient low-level matrix computations.This is an important organizing concept that can lead to more efficient matrix algorithms.

For each important algorithm discussed, the authors provide a concise and rigorous mathematical development followed by crystal clear pseudo-code.The pseudo-code has a Pascal-like syntax, but with embedded Matlab abbreviations that make common low-level matrix operations extremely easy to express.The authors also use indentation rather than tedious BEGIN-END notation, another convention that makes the pseudo-code crisp and easy to understand. I have found it quite easy to code up various algorithms from the pseudo-code descriptions given in this book.The authors cover most of the traditional topics such as Gaussian elimination, matrix factorizations (LU, QR, and SVD), eigenvalue problems (symmetric and unsymmetric), iterative methods, Lanczos method, othogonalization and least squares (both constrained and unconstrained), as well as basic linear algebra and error analysis.

I've use this book extensively during the past ten years.It's an invaluable resource for teaching numerical analysis (which invariably includes matrix computations), and for virtually any research that involves computational linear algebra.If you've got matrices, chances are you will appreciate having this book around.

Reviews (20)

Excellent!
This is probably the best book on linear algebra I have seen.

It approaches linear algebra from a theoretical point of view (i.e. linear maps instead of matrices), it is not "watered-down", and yet it is accessible to undergrads. The key reason for this is because Dr. Axler has kept the book well-focused, has put in only the necessary results needed, and has tied these elements together clearly. I obtained the book, because like the author, I never liked some of the more standard proofs of "classical" theorems. However, even the material at the beginning is superbly organized and well thought out, and a joy to read. His use of a single lemma in chapter 2 for example, (the so-called "linear dependence lemma") makes many of the results given later on in the chapter (and the book), trivial to prove. One of the reasons Axler can use this lemma so effectively, is because he is careful about his notation, and uses ordered tuples instead of sets of vectors. This is just one example of where his care in such matters pays off immensely for the reader.

I agree with one of the earlier reveiwer that his use of side-comments, though uncommon in texts, is very helpful and enjoyable.

Also, even though the book is not application oriented, Axler does give a lot of examples of abstract defintions, which for someone learning linear algebra, is essential to have. He ties new abstract notions, like say linear maps, to things that an undergrad with modest math background would understand (like derivatives, etc). These examples I think are also crucial to a good abstract math book. Too often, an abstract math book will go from theorem to theorem. In this book, I felt like I was pacing myself. There were a lot of theorems that followed sequentially, but there were also "breather sections", where Axler will stop and take a look at what he is doing. This, I think, gives the student time to stop, reflect on what he is doing, and get a better, deeper, fuller understanding of the material.

If you can purchase one book on linear algebra, this is the one book I would suggest!

Elegant theoretical presentation of linear algebra
This is a short, elegant presentation of linear algebra appropriate for upper level undergraduate math majors with a theoretical bent.The student has perhaps taken a linear algebra course designed for engineers and scientists.Such a student is comfortable reading mathematics and writing proofs.It is meant to be read and re-read until the ideas are absorbed.The exercises are relatively easy and no answers are provided.With exercises of this sort you generally know if you are on the right track and they require you to understand the presentation in the text and process the ideas in a straight forward way.

Of course, there is nothing in this book about applications or the computational aspects of applying linear algebra.

The price is right.This could be a very useful purchase even if it's not assigned as a text.

Reviews (53)

Great book, very insightful
I'm shocked at the number of negative reviews of this book. I think it's a great book. Linear algebra is an incredibly important subject, for example in my field of electrical engineering. Every time I need to refresh my understanding of a concept, I turn back to this book (I have the edition from 1976). I had Strang as a lecturer at MIT in the late 1990s, and he is a great teacher, which I think is reflected in his book. I truly enjoy reading this book -- practical, conversational and enjoyable to read, helpful insights, as well as Strang's opinions on the usefulness and practicality of various results. I would describe the book as an advanced introductory linear algebra book, if that makes sense. It's definitely not graduate level, but unless you're pretty sharp, it might be a tough first book from which to learn linear algebra. Maybe that's why there are some negative reviews of this book here. I recommend it very highly, especially for those who already have some knowledge of linear algebra. In fact, the reason I came to this page in the first place is to buy a second copy of the book, so I can have one in my office and one at home... there aren't very many books I would say that about...

First "...and its Applications" Book I Met True to the Title
Firstly, this book is true to its title...

It motivates the subject matter clearly and presents instances of why a certain type of problem is important (Why do we care about Ax=b, Ax=[lambda]x, ...)
It motivates the use of certain algorithms (Why do we use Gaussian Elimination, why pivot, why do the SVD, ...)

Also, as a basic text in Linear Algebra, which is THE introductory subject to applied mathematics, it serves a a primer for various areas in applied math: optimization, numerical solution of PDEs, "curve fitting" =), etc.....