Linear Algebra and Its Applications (3rd Edition) Description:

Linear Algebra and Its Applications (3rd Edition) review:
4 stars (Lay does a nice job.) - As other reviews have mentioned, Lay does a fine job of presenting topics that should be covered in a one semester Linear Algebra course. The text is easy to read and laid out nicely. Lay also does a nice job in balancing applications and concepts. The exercises apply to the section they are in, and do a nice job introducing students to simple proofs.



As another reviewer has mentioned, the invertible matrix theorem is never summarized and is instead scattered throughout the book. This makes the text less useful when a student wishes to refer to it for reference later in life. The answers in the back of the text often refer a student to the study guide instead of giving an answer. Some may see this as an advantage, I saw it as an annoyance. There is also a major error with how vector spaces are defined (the additive identity element is not defined correctly). Finally, although this text will suffice for math majors, but math students may want a more involved text. Many of the proofs for theorems could, and I believe should be left as exercises for students majoring in mathematics.



In conclusion, Lay's text will do a fine job as a self study text or a compliment to any linear algebra course, especially a course for non-math majors.
4 stars (Nice Introduction to Linear Algebra) - Many people may say what they want about this book. They will say that it was confusing or it presented proofs that could have been presented better. I have used this book extensively and have read it and done problems in it. The problems range from easy to very difficult. This book tends to be proof-oriented and problems within the text require students to construct logical arguments demonstrating some nontrivial fact (a proof). The author is condescending at times, placing the usual phrases like "it is eacy to see" within the text. My main problem with the text would have to be lack of depth in the explanations. Lay is purely abstract for the most part and doesn't want to use geometry or other didactic techniques relying on intuition, perhaps. I have heard of another text in linear algebra that does this. However, Lay isn't trying to make anyone an overnight expert. The text is probably reflective of his personality; he is stuffy.



I can understant his lack of emphasis on geometry though, assuming that the student has had only one calculus course. I would have to say this book gives you a fine education on the subject, but it doesn't attempt to give you a first-class one. I don't think first-class means more stuffy, but what I mean is more instructive in the underlying philosophy of the subject and its relations to Calculus.
2 stars (Too much theory, and confuses vectors with matrix operations) - Honestly, I would have never known that there was a better way to do this if I hadn't had to drop this class last fall for medical reasons, then retake it this spring with different prof. and different book. This d____ed book goes out of its way to make things confusing, causing too much memorization, and intertwines what a vector space is with matrix operations. It really does not have to be this confusing. Further, the guy does not teach you how to do proofs, but then requires you to do them in homework. He doesn't teach you where to start from, or what to think of when doing a proof. Linear Algebra is a tough class to begin with. It is known to be abstract and theoretical. Lay does not need to make an already challenging subject more challenging by presenting it in such a confusing way. Thank God I had to drop last fall. I'd have gotten a C or a D (and I'm a straight A student) if I'd had to stick with the Lay book.