Rating: 
Summary: An excellent linear algebra textbook
Review: I certainly agree with the other reviewers, Strang's text is clearly one of the best out there. It is definitely the best textbook I've seen on the subject. However, there are some flaws. It is quite obvious to me, after reading the book, that Gilbert Strang is a genius. Because of this, he sometimes loses the reader. His examples are terrible. I feel like saying "why don't you just DO the problem!?!" when reading through the examples. The solutions do not help one bit. There are certainly times when "number-crunching" would be preferable to abstract reasoning, particularly in the case of Gaussian elimination, calculating deteriminants, finding nullspaces, and calculating eigenvalues/vectors. Strang doesn't even SHOW how to calculate the eigenvalues/vectors but rather describes it in vague terms that are difficult to understand. Still, the book has it's merits. It provides a reason for everything in linear algebra. His applications to geometry are particularly helpful. Overall the book is excellent.
Rating: 
Summary: If you could bring only one Linear Algebra book to an island
Review: I checked this book from a library and liked it so much, I went out and bought a copy. Then I got his other book, the one on Applied Mathematics. Too many math books are afraid to give opinions. Not this one. Strang tells you what methods are practical, which are "ivory tower". Most other books I've seen dealing with linear algebra are uncritical and unnecessarily abstract. So much so that I've heard classmates describe linear algebra as "mystery math". Well, Strang is a breath of fresh air. His conversational style keeps your interest up. If you like stilted English, don't buy this book.
Rating: 
Summary: treats the subject frivolously
Review: I found several serious flaws with the text. It's too easy. There's too much filler. I learned almost nothing from it. To be sure, Strang has some interesting sections here, but he spends roughly half the book on talk, and the other half on linear algebra. Also, the text just seems like it's devoid of any serious material. It's too easy, and I was a complete beginner in linear algebra. Finally, it's completely useless as a reference because a lot of new ideas are presented in the exercises, where they are difficult to find when you are searching for some particular topic.I would recommend "Linear Algebra" by Friedberg, et.al.(isbn 0132338599) It costs the same, but I became quite an expert after reading it.
Rating:
Summary: Excellent Teacher
Review: I had the opportunity to learn linear algebra from Prof. Strang's online video lectures at MIT. This book will be a good comapanion to those lectures. All of you who hate Linear Algebra should take it from me : Watch the lectures along with the book, you will do no wrong. Strang's insights as he lectures, will make you fall in love with Linear Algebra.
Rating:
Summary: Excellent book for linear algebra
Review: I have had a linear algebra course and I have to admit it was not enjoyable becuase of the book. It was not understandlable and actually quite frustrating. Now when I am taking some advanced courses in Matrix Analysis I was looking for a book that would actually help me in the course. So I found this book and now not only that I enjoy linear algebra I really like it. Gilbert Strang's book really helped me out. Strang explains the concepts really as if we don't know anything about the course and then it goes into more complex situations. He covers everything that a beginner or an intermediate in linear algebra should know, and even he goes to explain some relevant applications of linear alegbra, such as to mechanical and electrical systems, dynamical systems... We can indeed see that Strang is a genius in this field and I think we can completly trust him as to what is written in the book. The book starts with some basic concepts of matrices, vectors and vector spaces. Then he goes on to describe the theory of linear independecy or dependency, determinants, symmetric matrices, Factorization, transposes, permutations, application and theory of column and null spaces, left and right inverses, complex matricesm eigenvalues and eigenvectors, Markov process, Fourier series, orthogonality, projection matrices.... The theory is well explained and combined with an appropriate example. There are plenty of exercises at the end of the chapter where the odd ones have answers in the back. If you are planning to are taking linear algebra course I would strongly recommend this book. It is not for an advanced linear algebra reader, but it is certainly for a beginner or an intermediate one.
Rating:
Summary: Great text for a first year course in linear algebra!
Review: I used this text for my first class in linear algebra. I agree with the other reviewers on average. This is a great text for a first class, although I feel that for a highly motivated class, 'Linear Algebra' by Hoffman and Kunzeis the ideal text. Dr. Strang's style make his text very enjoyable to read. The proofs are there, mostly. And the proofs are just perfect for a first class, not to rigorous and at the same time, not too buttered up. This text is very versatile. It can be used for a intro to higher math, self-study, or for physics and engineering students. Honestly I am leaning toward 5 stars, but I feel that there are texts which are superior to Strangs', so in fairness to those texts I rate this text 4 stars.
Rating:
Summary: Disappointing
Review: I was disappointed. Through the middle of chapter 3, the text was excellent, than the end of chapter 3 was totally cryptic. Chapter 4 was ok, so was most of chapter 5, but chapter 6 and on was just horrible. I couldn't understand a thing. SVD is not explained in any detail, neither is Jordan form. This book is a waste of money, since only about half of it is good and the rest is useless. I'd recommend Howard Anton's book, it costs less, and there's much more material in there.
Rating:
Summary: a good impression
Review: I wondered how this book could elicit such mixed opinions, so I took a quick look by reading the first few pages, and scanning the first couple chapters. One can already see the writing style resonsible for this.
Strang is trying to clearly explain the ideas behind the various mechanical constructions, such as Gaussian elmination, in terms of their interpretation via matrices, and also explain practical aspects of the constructions such as cost of implementation, efficiency, and tendency to go "wrong" under roundoff.
This is a lot of ideas to put in a few pages, and students used to books which merely display a mechanical operation, then drill it over and over, are likely stunned by the compactness of the presentation. They are not used to mulling a few succint phrases for meaning, and taking their time. One student reviewer even complained that he had to reread after a few paragraphs, as if that were a bad thing.
He does give very clear and simple examples, he just doesn't give a lot of them. When he has made his point, he does not dwell on it, he moves on to enhance and deepen it. Probably you should work every single exercise in this book.
This is obviously an excellent book from which to learn a lot of deep useful insights into linear algebra and its uses. For those who want more drill on the arithmetic involved, any other book will have a lot of that. But those books will not have the clarity and focus of this book, in most cases. I recommend it highly.
Rating:
Summary: A great book
Review: I'm not really sure why people dislike this book. In general, Strang writes some of the best mathematics texts out there, and this book is no exception. In fact, my only objection to this book is that it is too introductory, as is _Intro to Applied Mathematics_, but they aren't after all intended for graduate courses. The one thing I really enjoy about his texts is that his writing, even on basic material, sometimes contains very deep insights into the underlying structure of the mathematics. Understanding a Strang textbook is the difference between actually _understanding_ mathematics and just being able to do it. So I heartily endorse this book. If you want a higher-level text, I'd suggest Demmel's Applied Numerical Linear Algebra. But reading this book still wouldn't hurt.
Rating:
Summary: Best linear algebra book I've seen
Review: I've seen many linear algebra books, and none are as good. They all lack the rigor and detailed explanations. Strang doesn't just give you a definition of a determinant, for example, he walks through its construction by starting with a few simple properties. If you ever wondered where all those matrices and matrix operations come from...what's behind that stuff? This is the book for you. The first 5 chapters are the main course describing all the details, and the last 3 chapters give some applications, including descriptions about how to compute with matrices...useful if you are a programmer.
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