Rating: 
Summary: Wonderful learing experience
Review: I really enjoyed learning from this book. Not beeing a keen reader I was very impressed with the conciseness and clarity of the text. There were many clear examples in the text. I found the question at the end of each chapter helpful for reviewing the new information. What I would have liked to see was the answers to the odd numbered multiple choice questions at the end of the book. And perhaps a discussion sumary of the main points at the end of each chapter. Over all a very impressive book.
Rating: 
Summary: Easy to read
Review: I really like this book. He explains everything very clearly and concisely. This would be a good book for someone interested in Linear Algebra to read. The exercises are not simply computational, but he makes sure you understand the theory behind the math as well. The odd answers are in the back of the book, and on some of them he will give you hints instead of the answer itself. The one problem I had was that sometimes the exercises did not follow from the examples in the sections, but those were few and far between. Another thing: there are quite a few proofs as exercises so if you are not familiar with math proofs you may want to look at a book dedicated to proofs.
Rating:
Summary: Great Book
Review: I really like this book. It is clear, accessible, and the exercises are great. I highly recommend this book for those interested in learning linear algebra especially from an applications perspective. Also very good for self-study.
Rating: 
Summary: Jumps around and Lacks important information
Review: I think David C. Lay does not try to help the student with this book. Instead, he wants the student to work for the solution. This is fine some of the time, but not all of the time. I think this book was written from a perspective that most students already know what he is talking about. The examples are inadequate for the problems in the book and the solutions guide always says something really helpful like, "Look in your textbook for the answer". I like Linear Algebra, but I don't like getting the run around when I get lost. I am using Elementary Linear Algebra by Ron Larson and Bruce Edwards as a supplementary text and it will be the book that I keep after the course is over. On the other hand, Lay's book is going back to the campus bookstore.
Rating:
Summary: One of the greatest books!!!
Review: I used it in a linear algebra class when I was an undergraduate at Cornell. I found out that it was a very readable and useful reference for concepts and theories. The book is very organized; and it's such a good start for people who are interested in learning linear algebra. Believe me! U won't be disappointed!!!
Rating:
Summary: A nice introduction to the subject
Review: I used the book to review the linear algbra that I had taken 16 years ago and this book adequately served this purpose. The book provides many examples and provides enough information to understand the mechanics of linear algebra. The theory is sometimes a little light, however that should be expected from an introductory linear algebra book. Overall a good introduction to the subject and an excellent refresher for those seeking one. A few notes on the study guide - it would be more helpful if more problems were worked out. Also, some of the theory that I would expect to find in the text is only in the study guide.
Rating:
Summary: Very readable text
Review: I used this as the textbook for an undergraduate course in Linear Algebra. It was by far the most reader-friendly math book I've ever had the pleasure of using. The book explains Linear Algebra in plain, easy-to-read english. Each section of each chapter is very clear and to-the-point. The examples are helpful and well-placed in the chapters. I attribute getting an 'A' in that class to this text. One word of advise however... the study guide for this text comes in handy at numerous points of the book. It's not needed, but strongly advised. Other than that, the book is great! I only wish that I had a calculus book that well written.
Rating: 
Summary: From an instructor's point of view
Review: I used this book for several years in my Linear Algebra. It suffers from many of defects that all Linear Algebra texts at the level suffer from these days. The first Chapter introduces the concept of linear independence without suitably introducing vectors. Linear transformations are also introduced in this chapter, again without the proper tools to deal with it. Another topic in this Chapter is the solution of systems of Linear Equations. The treatment of the case where there is more than one solution is totally and hopelessly inadequate. The method used to generate the solution does nothing but confuse the students. Chapter 4 is far too laconic. The treatment of projections lays no foundation, does not connect it with eigenvalues but just jumps into orthogonal bases. It is difficult believe that anyone would guess that orthogonal matrices are important from the information given in this book. The treatment of least squares is too sparse. The treatment of Linear Transformations is extraordinarily lacking. The treatment of the kernel and image lead no place. There are insuffient number of examples and relation to geometric concepts. Unfortunately, almost all new texts in this field are just as bad.
Rating:
Summary: A Decent Reference Tool for Economists
Review: Lay presents here a basic textbook on linear algebra. Topics covered include matrices, determinants, vector spaces, eigenvalues & eigenvectors, and orthogonality. As a student of economics, I was happy to see that a few of the applications of linear algebra presented are related to economics and statistics (the Leontief Input-Output Model in Chapter 2, for example). When I first encountered this book in an undergraduate matrix algebra course, I found it to be quite accessible despite my liberal arts background. More recently, since I have been a graduate student, the book has proven to be a decent reference for the basics of linear algebra, although I wish it covered projections in more detail -- particularly non-orthogonal projections. From an economist's point of view, I would sum this book up as follows: it covers enough material to address linear algebra concepts needed in a first-year graduate microeconomics course, but not enough for a first-year graduate econometrics course.
Rating:
Summary: A Decent Reference Tool for Economists
Review: Lay presents here a basic textbook on linear algebra. Topics covered include matrices, determinants, vector spaces, eigenvalues & eigenvectors, and orthogonality. As a student of economics, I was happy to see that a few of the applications of linear algebra presented are related to economics and statistics (the Leontief Input-Output Model in Chapter 2, for example). When I first encountered this book in an undergraduate matrix algebra course, I found it to be quite accessible despite my liberal arts background. More recently, since I have been a graduate student, the book has proven to be a decent reference for the basics of linear algebra, although I wish it covered projections in more detail -- particularly non-orthogonal projections. From an economist's point of view, I would sum this book up as follows: it covers enough material to address linear algebra concepts needed in a first-year graduate microeconomics course, but not enough for a first-year graduate econometrics course.
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