Linear Algebra and Its Applications with CD-ROM, Update [Hardcover]

I am just finishing up an introductory Linear Algebra course using this book. I am a mechanical engineering student, and not a math major, so keep that in mind when reading this review.

I personally really liked Lay's approach and writing style. The first chapter is a basic overview of linear algebra and helps you start to see what linear algebra is all about immediately.

I also like Lay's method of highlighting important theorems and definitions. He uses a light blue background for theorems and key ideas and a greenish type color for definitions. Very helpful for studying and you don't have to dig through the text to find the main topics. There is also a glossary, something that seems kind of rare in math textbooks and I really liked having.

I liked the practice problems before each problem set, they were kind of like examples, except the solution was on a different page. Also, row operations in this text always work out nicely, which means I didn't struggle with difficult computations that need not be difficult and cloud the concept I was trying to learn.

I didn't feel like there was enough problems. For each section there was about 10-20 problems computational problems, some true/false questions, and about 10-15 or so questions that either asked you to prove things or were applied problems. I wish there was twice the amount of problems, I'm the kind of student who needs lots of practice.

The invertible matrix theorem should of been summarized in its entirety somewhere. Its scattered across 6 sections in 5 different chapters.

I feel the book is really good for engineering students and applied math majors. Pure theoretical math majors, I could see how you might not like this book. The text doesn't seem that abstract and you aren't buried in proofs, but I believe Lay has geared his text more towards applied mathematics than pure math anyways. I was able to learn most of the material on my own as my professor (as in most math and science classes) was really bad.

In summary, I feel that this book is good for self-study or as a saving grace from a poor professor.

I'm familiar with three linear algebra textbooks: Gilbert Strang's Linear Algebra and Its Applications, Georgi E. Shilov's Linear Algebra, and now this one. It was recommended to me by one of my brothers, who had the author as a professor at the University of Maryland - College Park.

Gil Strang's book is very well regarded, and I like it, too. However, as a writer, Strang tries a little too hard to be friendly and colloquial. As a result, some of his explanations are less clear than they need to be. It helps that videos of his linear algebra lectures are on the Web at [...], and those lectures clarify some of the "folksy" wording in the textbook. Strang obviously loves his subject and knows it thoroughly, but those qualities, however admirable, do not substitute for clear writing.

Georgi E. Shilov's book is also highly regarded, by me as well. Shilov is one of those no-nonsense Russian mathematicians who's all about the subject and doesn't care if you like him or not. As a result, his writing is very clear and straightforward, albeit a little stiff and formal even in translation. The great virtues of Shilov's book are that the writing is clear and it's very rigorous: in fact, a reader would do well to have some familiarity with abstract algebra before starting it. But the book's virtues are also its weakness: because of the rigorous treatment, Shilov offers considerably less conceptual hand-holding than Strang. Yes, you can understand what he's talking about, but you'd sure better have a strong mathematical background, time, and self-confidence to plow through his book, especially if it's on your own.

Which brings us, finally, to the Lay book. I am delighted to report that Lay combines the informal, encouraging tone and conceptual hand-holding of the Strang book with the clarity of the Shilov book. In other words, they're all good, but for most undergraduates, Lay is the best of the three. There's also an excellent study guide (Linear Algebra and Its Applications: Study Guide (update))for the Lay book.

I have heard students complain about how unhelpful this book is and professors complain that it is too easy.
I strongly disagree with both.

I am very well acquainted with the following introductory texts: Strang, O'Nan, Leon, Larson and Lay. As a student, I learned initially from the O'Nan text, then transferred colleges and had to repeat the class with the Strang text. As a professor, I have taught out of the 3 remaining texts. I have also examined the text written by Kolman.

Lay's Ch. 1 is an extraordinary result: he creates an overview that unites all the main ideas that comprise linear algebra.
No other text I know of comes near the breadth or clarity he achieves in this opening chapter. This chapter alone makes the book worth owning.

I also want to answer those who attack the Student Study Guide. It one of the few I have seen that is actually written by the author. It is likewise excellent and provides answers and hints for all the most critical problems in the text. I highly recommend it as well. I require it when I teach using the Lay text.

I have convincingly achieved my best classroom outcomes using the Lay text. I have actually covered most of the first 6 chapters and the first 2 sections of Ch. 7 at the junior college level in one semester with a decent group of students who were often slowed down by a group of underachievers in the class.

In summary, students who do not like this book will be hard pressed to find anything better- just pick up one of the competing texts used in colleges today and try to read it. Lay is by far the most 'user-friendly' text, he is clearly attempting to engage his readers. Unfortunately, most students at this level do not have enough experience at this point to make an informed judgement about the quality of a mathematics text or the quality of a mathematics teacher.

Professors who do not appreciate this text are an even more puzzling group. I can only surmise that the teachers in this group do not understand the ideas or the focus of an introductory class in linear algebra very well and are simply teaching without thinking.