Elementary Linear Algebra

I used this in my undergrad course as a math major at UT Dallas. I really enjoyed it; the book has sections on applications in just about every chapter, and there are lots of computational exercises as well. In addition to answers to odd-numbered exercises, each chapter has a "self-test" with all the answers provided at the back of the book. It's a bit chatty, but that befits an undergrad text.This is a good book for self-study, though if you are really serious about it, you might want to supplement it with a more rigorous reference (the Dettman text is good for this).

I must say I have been pleasantly surprised with this book. I find it very readable. It has been very easy for me to teach myself what I need to know right out of the text. There aren't many math books I've found that can make that claim. I haven't needed to consult any other books to understand the material. The only real improvement I could wish for from this book would be a solutions manual.The book follows a very logical progression. Each topic builds on previously covered material. It's clear to me now why UT chose this book for its math major classes. The emphasis in this book is teaching you to think abstractly and work out difficult proofs, which you're going to need for more advanced math classes. The book has a lot of proof exercises (but there are a lot of computational exercises as well.) In all, I'd say this book does a great job doing what it was designed to do, which is to train future mathematicians. This naturally implies, however, as a previous reviewer stated, that it's going to be short on applications. So if you're going to be taking a class using this book, it would be a good idea to learn a little about the applications of linear algebra before you start, if you need that knowledge to keep yourself motivated. Then prepare to learn linear algebra from a very fine book.