Rating: 
Summary: A terrific book on linear algebra
Review: LINEAR ALGEBRA, Third Edition, is one of the better books on linear algebra. The material is presented in an abstract and mathematically rigorous fashion. The focus of the book is on the ideas and proofs behind the linear algebra -- its treatment of applications to physics and computer science is almost nonexistent. Topics covered include vector spaces, linear transformations, systems of linear equations, determinants, inner product spaces, eigenvalues and eigenvectors, and canonical forms.For the aspiring engineering or computer science student, this book is not for you. Basic matrix theory is enough for those fields, and this book is littered with rigorous proofs. There are many other textbooks that present linear algebra from more of an engineering or computer science perspective. As an alternative I recommend that you take a look at "Matrix Analysis and Applied Linear Algebra" by C.D. Meyer. The style of this book is written in the traditional theorem-proof-example style and is thus geared more towards aspiring mathematicians, especially those who enjoy theory and pure mathematics. Many of the examples demonstrate less than obvious inferences and can be very useful, but of course the meat of the book lies in the comprehensive build-up of linear algebra theory from a mathematically sophisticated point of view. In summary, a highly recommended purchase for mathematicians. Computer scientists and engineers should look elsewhere though.
Rating:
Summary: Good book on linear algebra
Review: Many linear algebra books start out with "this is a matrix" and "this is how you multiply matrices." Some people may find these books to be nice and concrete: easy to work with. I, on the other hand, hate memorizing pedantry, and prefer to look at actual substance--the reasons behind the concepts. This book does a good job of illustrating the concepts, and gives sufficient examples to aid in illustrate the import of concepts. Linear algebra is mainly about vector spaces and linear transforms. This book does a good job of telling the enthrauling story of linear algebra. I took this class from Dr. Friedberg, and he is an excellent speaker. This shines through in the book. With regards to another reviewer: If you try to learn mathematics by memorizing proofs, then I don't see how you can every get anything done. Mathematics is about learning paterns of reasoning and proof; not memorizing facts and proofs of them.
Rating:
Summary: One of the best linear algebra texts available
Review: One of the best linear algebra expositions, however I would advice some familiarity with matrix algebra and modern algebra before attempting to read this book. The book emphasizes abstract vector spaces, giving special attention to the relationship between linear transformations and matrices. It covers all main subjects in linear algebra from invariant spaces to canonical forms and includes applications to numerical analysis (condition number),statistics(markov chains), and linear differential equations.
Rating: 
Summary: Sufficient for Supplement
Review: Reviewer Background:
I had exposure to problems involving to R3 vectors and planes in high school. We used this text as an introductory linear algebra course for the advanced section at University of Waterloo. We used his text primarily as a reference text and a source of problems.
Comments:
In the context that we have used it (as a reference) text, I disagree that the text is pedantic. I think that having the simpler proofs in the text reduces the learning curve and introduces the student better to the more rigourous ways of thinking. Because we had the benefit of an instructor, I didn't find it a disadvantage that some of the less trivial problems were exercises. On the other hand, I could see how this may lead to problems without an instructor. Fortunately, all the necessary (marked with a dagger) results that were left as exercise weren't particularly challenging. For certain proofs on assignments, it is insightful to look through the text for methods of explanation. (For me, ) In linear algebra, learning to write precise concise prose was a non-trivial task. The examples presented in this book facilitated that learning process.
Rating:
Summary: awesome...i'd give 10 stars
Review: This book combines a very rigorous treatment (with a flavoring of abstract algebra) and interesting applications. The presentation is very clear and straightforward. You get theorems, a proof of each one, and curious exercises. Some exercises also challenge you to develop and prove results about some side topics. As you go through the chapters and learn more, you prove further results. Also, this book is the first which presented Jordan forms lucidly and thoroughly. Other texts shove it into the appendix, which is a mistake, since this topic is important. Finally, the applications are plenty. Standard ones like Markov chains, plus a few fascinating applications, like an entire section devoted to the development of the basics of Special Relativity. This should be the standard text on linear algebra, instead of that drivel by Strang.
Rating:
Summary: Beautiful presentation !
Review: This book has a lucid treatment of the matrix theory and linear trnasformations of differential equations. although the applications are extended upto Hamiltonians, Markov chains and relativity to name a few. All in all an excellent book which prepares the reader for more specific topics according to reader's taste. Worth reading is the 6th chapter for advanced students intending to major in physics or maths. Definitely worth having one in your shelf. Clear presentation and ample examples will encourage your appetite for matrix theory etc.
Rating: 
Summary: Linear Algebra: Friedberg
Review: This book is not that good because it proves many useless, or near trivial theorems, then leaves the more interesting and deeper theorems as homework exercises. I would go with the Kenneth Hoffman: Linear algebra book instead. David
Rating:
Summary: Almost perfect
Review: This book presents a very rigorous and comprehensive development of linear algebra. With a certain level of mathematical maturity, a reader can study this book even if they do not have prior exposition to the topic. The discussion is as general as possible, stating theorems for abstract vector spaces (infinite dimensional where possible) defined over abstract fields. The number of lemmas, theorems, and corollaries in the book is amazingly high. Consequently, many of the proofs are elegant and concise since they can rely on a lot of the results previously established. The only thing that I'm disappointed with in this book is the development of diagonalization, which is why I gave it 4 stars. The text relies on determinants to define the characteristic polynomial and to ultimately discuss diagonalization. Diagonalization is important in studying canonical forms and linear operators on inner product spaces, so it should have been developed with a more self-contained manner for the sake of elegance. However, I should note that some of the exercises throughout the book form sequences which lead to results not discussed in the main text. With the right choice of exercises, it is possible to come up with a determinant-free explanation of diagonalization, but this requires great effort on the part of the reader. Overall, I highly recommend this book to someone who wants to have a solid understanding of linear algebra.
Rating: 
Summary: Not for me thanks...
Review: This is not a book to learn linear algebra from... this is a book to help you formalise your existing knowledge. The book is very formal and rigorous, often concentrating on giving trivial proofs in a pedantically rigorous fashion, and leaving the important concepts to the exercises at the end. I see this was a concern of other reviewers too. I must agree that the presentation is consistent and clear with the "theorem-proof-example" model used throughout. The examples however are often too trivial in most cases to truly illustrate the power of the concept, and to bridge the gap between them and the end-of-section exercises which I found generally too advanced and often removed from the content of the actual text. I have degrees in both engineering and mathematics, and I really disliked this book from a student's perspective, and found it really hard reading. The examination at the end of the course could really only be a request for regurgitation of proofs, and the sheer number and rigour of these made it a book from which I gained very little. Not for the feint-hearted.
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