What topics/chapters are covered in a typical linear algebra class? I am a physics/math major but I won't be able to take classes for a few years. I am trying to teach myself linear algebra so I can read physics textbooks. Thanks
I should have mentioned determinants as well. If you understand these things, you're off to a good start. I've been told that Friedberg, Insel & Spence is a very nice book. Axler is also good. There are several other acceptable choices. I would however recommend that you stay away from books like Anton, which wait as long as possible with the introduction of linear operators (also called linear maps, linear functions or linear transformations). The sooner they are introduced, the better.The concepts from linear algebra that you need to understand are: vector spaces, inner products, linear independence, orthonormal bases, linear operators, matrix multiplication, the relationship between linear operators and matrices, the adjoint operation, eigenvectors and eigenvalues.
This is the best linear algebra book I know of, and it also happens to be free: Hefferon, http://joshua.smcvt.edu/linalg.html/ . "Best" for me means interesting applications and good motivation for new topics as they're introduced.