TITLE: Prerequisites/Books for A First Course in Linear Algebra
QUESTION [18 upvotes]: What mathematical knowledge do I need to begin studying linear algebra? In particular, how much calculus do I need to know?
Also, do you have a favorite linear algebra book you can recommend?

REPLY [8 votes]: I'm surprised nobody has metioned Axler's Linear Algebra Done Right. I think this is a perfect book for a beginning student of mathematics who is interested in learning to do proofs. Axler is very clear and careful in his explanations and although there are some sections toward the end where calculus would be useful, these can be skipped on a first reading and revisited once you have calculus under your belt. 
Now, while Axler is very good and gives you a firm grounding in the basics, it is not comprehensive. If you really like linear algebra and want to dive deeper, you might want to explore Roman's Advanced Linear Algebra. It is quite a bit more advanced than Axler and presupposes much more mathematical maturity, although technically it is self-contained. I think once you digested everything that's in Axler though you would be in a position to start looking at it.
If you still haven't had enough linear algebra after all that, you could survey Greubs' Linear Algebra and Multilinear Algebra. There is a considerable overlap between Greub's Linear Algebra text and Roman's but in my opinion Greub takes a little more effort to read. In his multilinear algebra text, however, you will find topics that are rarely covered elsewhere. Unfortunately, it is out of print but Google here is your friend.