Rating: 
Summary: A mysterious little book that is witty and a tad playful...
Review: Lay's teaching structure is phenomenal. In other books on the subject, key topics such as linear independence and the invertible matrix theorem are merely mentioned rather than focused upon. But Lay states concepts clearly, building technique upon fundamentals to essentially ingrain concepts. However, though for the most part good, this text has its flaws. Linear transformations are tersely covered, and eigenvectors more so, leaving the readers dazed by chapter six. Nevertheless, on the overall scale, this book is excellent and should find a warm nook in every mathematician's heart. Bravo, Lay! Bravo!
Rating: 
Summary: Avoiding the Brick Wall
Review: Linear algebra is relatively easy for students during the early stages of a course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a "brick wall". Instructors seem to agree that certain fundamental concepts (such as linear independence, spanning, subspace/vector space, and linear transformations), are not easily understood, and require time to assimilate. Yet students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete R^n setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible because they are familiar. This is the only introductory linear algebra text that allows students to avoid the "brick wall."David C. Lay holds a Ph.D. from UCLA and is Professor of Mathematics at the University of Maryland. He has over 30 research articles published in functional analysis and linear algebra, and as a founding member of NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current modernization of the linear algebra curriculum.
Rating: 
Summary: Very reader friendly
Review: Math texts are notoriously poorly written and difficult to follow for the typical undergrad without the guidance of a professor. This book is an exception to the norm. Not everything, but most things, are presented in a way that most students will be able to absorb on their own.
Rating:
Summary: Pretty decent
Review: My only real complaint was that it did not go into the depth that some of my later classes required.
Rating: 
Summary: Poor book
Review: Not a good text. Even with the accompanying study guide most of the problems are only briefly explained. Multiple choice "did you read it" questions, often full of hidden word traps, are not directly answered in the book.The study guide merely refers the reader to a vague paragraph and page number. This strategy ignores the obvious fact that if the reader got the question wrong they clearly didn't understand that paragraph in the text.
Rating:
Summary: The best linear algebra text that I've taught from
Review: Students in my linear algebra course have typically liked this
book.
From my perspective as an instructor, I like the order in which
topics are presented, the emphasis on reasonable use of technology, and the depth of the material, which is just about
right for our course. However, some sections are not as clearly written as others, and because there is too much material for a one semester course, the instructor has to carefully pick which sections to cover.
Rating: 
Summary: Good book gets knocked down by poor answer/study guide
Review: The book is good, probably better than I think. I blame much of my bias on the (visiting) prof I had for this intro class. She didn't like the way the book was organized and insisted on jumping around - quite a difficult way to use a math text unless you already know the material.
I didn't think the organization was bad. As an undergrad econ major I understood the progression. Unfortunaely I think the coverage in some areas is too concise and sometimes the book fails to tie ideas together. As someone else noted, the proofs are passable but not great. The book lends itself to a variety of majors, whether math, econ, physics, business, etc. as there are a number of good examples.
My biggest gripe is with the answers in the back and the answer/study guide. I'm sorry if Dr. Lay's students are too lazy to actually do the work and reading and would prefer to look in the back, but christ allmighty, please provide the answers *and* reasons for the answers for T/F questions. If the T/F questions are important enough to include in virtually every section then don't you think we should have the answers? The answer/study guide is virtually worthless. Look, I played the game and plunked down the extra bucks for the study guide, so would you please give me the solutions? I don't like getting the run-around if I don't understand something. Using the guide is like something out of a monty python skit. So for these reasons the book gets rated down a star.
Rating:
Summary: Recommended for everyone!
Review: 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. 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: Plain English makes Linear Algebra easier to understand
Review: The proofs, explanation, and examples in this book make those theorems easier to understand. The true-false questions in the problem sets are also helpful to test if a reader really understands the text. However, I found the solution manual wasn't very useful. I would go to my professor or someone else to find out the answers.
Rating: 
Summary: Not very thorough
Review: This book is not very thorough. Most of the examples are near impossible to do without a previous knowledge on the subject and other resource material. The solution's guide explains every 7th odd problem, which is extremely frustrating as well. The course material goes much too quickly. DON'T BUY THIS BOOK! It's just not worth it.
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