Rating: 
Summary: shallow, too long, clumsy
Review: This book is one of the worst mathematical texts I have read. When I told my student counsellor so, he said "thank you".
The book is bad for mainly two reasons:
1. If you are an engineer, or want to learn the material just for the applications, and not to practice your mathematical skills. Then the book can be very frustrating. Many proofs are left as excercises and the material is scattered widely. I think its better that the text coherent, and that the book has good excercises.
2. If you want some depth this book is not for you. There are too many trivial problems and examples and the book could be compressed to less than half of its length.
The proofs are not the best. If I remember correctly some proofs are based on the algorithm of solving systems of linear equations, instead of quite simple use of definitions.
It also emphasizes on the wrong things.
Despite of its length it does not cover so much theoretical material. And Lay doesn't give a picture of how important some of the concepts are.
I also find it a bit strange that Lay includes two almost identical chapters... one about R^n and one about finite dimensional vectorspaces. The thing is that all finite dim. vectorspaces have the structure of R^n. And R^n is a finite. dim VS.
The only positive thing is that it gives a pretty soft introduction, and its not so hard-digested.
Rating: 
Summary: One of the best!
Review: This book is probably one of the best math books I have ever worked with. The last time I wrote a review for this book, I gave it 2 stars; now, after going through the whole book, I'm able to give it 5 stars. No matter what your major is, and no matter how advanced you are, this book has something to offer. It is example-oriented, easy to follow, and right to the point. Each chapter starts off with theory and ends with applications. Each section starts with basic definitions and easy problems and ends with theorems and harder probrems. The 2nd edition is pretty much the same as the 3rd edition, so don't waist money for nothing.
Rating: 
Summary: Good introductory book- Math students may want more
Review: This book presents, in a reasonably clear manner, the concepts, formulas, and theorems related to linear algebra. Examples of linear algebra in economics and engineering help solidify these concepts. However, the book does not cover several types of matricies. For example, an assignment involved a population-change question involving Leslie matricies. Unfortunately, the Leslie matrix is not covered anywhere in the book. It would also be desirable to have a summary of the Invertible Matrix Theorem. Instead, the various parts of this theorem are scattered throughout the book. Otherwise, however, this book serves its purpose well- as an introduction to linear algebra.More advanced students will want a text with more thorough coverage.
Rating:
Summary: It is a good introductiory book
Review: This is a very good textbook for whom doesn't have any matrix background. I like its contents because it is very colorful and easy to read. If you don't have any background about the matrix you should buy this book.
Rating:
Summary: Very Good
Review: This is a very good textbook to learn linear algebra from. It is actually fun reading parts of it! Lay takes great pains to give good examples and plenty of them. The solved practice problems at the end of each section are also very helpful. My only complaints would be that the book spends too little time on linear transformations and the important concept of whether or not they are one-to-one and onto. The book's treatment of change of bases is confusing at times as well. The study guide is also totally worthless.
Rating:
Summary: Good book (but nor geared towards hard-core mathematics)
Review: This is one of the better linear books that i have seen so far.
The examples are great and the illustrations give a good reprensentaions of complex mathematical thougt. The book develops at a rate which is an almost perfect rate. The only negative thing that i can reemark about the book is that it doesn't go into deeper ideas such as Complex matrices, inner products and Jordan-block matrices. I would reecomend this book for students studying engineering and buissnes but a longer, more challenging issue for mathematics students
Rating:
Summary: Excellent text for an introduction to linear algebra
Review: This text is a dream to read compared to many other mathematics texts. Lay's writing style is clear, and he rightly stays away from using wording that distracts the reader from the theory he presents. Mathematical notation is introduced before it is used, and proofs are placed in an appendix. Overall, this is a very good book for undergraduate study. It won't carry you through graduate classes, but it might be useful as a support book if you have a weak background in the topic. Math majors who love concise formalism and extended proofs should stay away from this book. Engineers, business, physical science, and social science majors will find the text very helpful.
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