Rating: 
Summary: Great Undergraduate Text
Review: Finding a good introductory text on Linear Algebra is hard to find. Most texts are either to low of a level to be interesting, or too high of a level to be accessible to an undergraduate. This books strikes a good middle ground. There are just enough abstract concepts to make the book worthwhile for the instructor and plenty of matrix theory and examples to engage the student. The true gold of the text are the appendices! Most books omit such material or treat it too briefly, however this book makes some very worthwhile discussion of some important material.
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Summary: First "...and its Applications" Book I Met True to the Title
Review: 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.....
Rating: 
Summary: Bad writing.
Review: Frankly speaking, Gilbert Strang's book is bad in writing. I think that the content is good but the way to write and explain is very hard to understand unless you have the concept of linear algebra already. All and all, good content but BAD writing.
Rating: 
Summary: not terribly interesting
Review: Granted, a couple things here are explained really well, but after reading up to beginning of ch.6 (i didn't understand anything afterwards) I don't feel like I've learned anything. Strang seems to spend more time on praising linear algebra than actually teaching it. Definitely not worth the money.
Rating: 
Summary: also see "Math Easy as Apples & Bananas" by Yasmin Khan
Review: Great book but considering the controversy and pain some people genuinly feel, I recommend the books by Yasmin Khan, "Math Easy as Apples and Bananas" as a first read, I have not seen anything easier in Applied Linear Algebra, with topic from Fast Fourier Transforms, Sin(x)/x, wavelets. Lets you learn in a few hours not days.
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Summary: Awful book
Review: I agree with the others who gave this book low marks. This is NOT a book for "introductory" algebra courses or for building a strong basic foundation for understanding the properties of matrices. Strang rattles off with obfuscating explanations as if you have already had a previous exposure to linear algebra and matrix theory. For example, just compare Strang's explanation of the least squares method versus the explanation in Harvey Gerber's "Elementary Linear Algebra", and you will see what I mean. Strang's explanation is hardly adequate, while Gerber's is superior, providing an easy-to-understand motivation for the subject, a well defined proof, and copious examples. (Gerber's isn't the only book out there; there are many, many other books that are far, far better than Strang's. ) For best results, if you are required to buy this book for a college course, buy this book "used" (to save money) or borrow it from sombody else (share with a friend?), and buy another book from which to learn.
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Summary: The right thing for engineers
Review: I agree. This is a great book to really learn linear algebra from. Especially for engineers, who are more interested in the "essence" of the subject, rather than the strict mathematical proofs and definitions. I have studied the book 4 years after studying linear algebra from a purely mathematical textbook, and I am not ashamed to say I realized my ignorance! Through this book I really learned what linear algebra really is about. I gained what you can call "intuition" in the matter, thus being able to predict the result of a problem without explicitely solving it.
Rating:
Summary: Good book
Review: I am a foreigner, graduated in UM, Ann Arbor years ago. I can tell the courses at MIT are better than ours in general. The book is much clear. Unfortunately, I did not have opportunity ot go to Stanford or MIT. (OK, we have many professors come from MIT/Stanford) Reading many American math books, most of them are quite weak. They emphasis on how to get answers (mechanically without thinking). Those book is for school and exam only. They have no real life value. At least after reading those books, you can say you know calculus etc. This book is not. This book reminded me when I was in my home county (HK), I read many high quality math books. MIT/Stanford courses are harder but they presented the materials and theories are much more clear (in general). In my opinion, one needs to be very good and experience enough to present the 'complicated' subject in simple way. I see many authors present the subject in 'circular' way or very 'unnecessary complicated way' (to impress the readers?!) or because they cannot see the simple way. The simple way does not mean the easy way. I just mean it is 'clean' and 'straight to the point'. The simple way will have a lot of insights and make the read think. This book is a good book. It does make you think and the author does not ask you mechanically to do the math without understanding the materials. Without a lot of examples, it is good for beginners.
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Summary: This book is for a serious student
Review: I am pained at the disappointing reviews submitted. Prof. Strang's work deserves better respect! I have used this book from 2nd edition onwards for students' perusing a course in Power System Analysis and Digital Protection. I recommend Matlab be used along with the course to understand the different processes in linear algebra, its relation with algorithm development in analysing various stability issues and methods that can provide dimensional reduction of the original problem. It takes time to absorb the work. But once completed, it is a poetry that one can never forget!
Rating:
Summary: The Best Book on Linear Algebra
Review: I appreciate the frankness of the author who feels that the subject is made too abstract.The unique feature of this book is that Strang tried his best to give a good physical picture of whatever concept he introduced in the book.That greatly aids in understanding of the subject.I never felt that I am reading a book rather I felt conversating with Strang.My request to Strang would be that he should make the excercises a bit diffucult.
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