Strang has another great book, Linear Algebra and its Applications: http://www.amazon.com/Linear-Algebra-Applications-Gilbert-St... Everything I know about linear algebra I learned from this book.

The Strang book is pretty much indispensable, I think.

http://www.amazon.com/Linear-Algebra-Applications-Gilbert-St...

The course lectures are online, too.

http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/Video...

I've been taking courses related to Machine Learning, and never having taken a Linear Algebra course, I find myself going to this text and watching these lectures a lot to bring myself up to speed.

My favorite text on Linear Algebra is Gilbert Strang's Linear Algebra and Its Applications although the current edition is ridiculously expensive:

http://www.amazon.com/Linear-Algebra-Applications-Gilbert-St...