In terms of books, I would say Linear Algebra Done Right. The book requires some background to understand efficient. But, once you have some background, it is very good for having a systematic and rigorous understanding of Linear Algebra theory
If you can handle it, fabulous.
If not, you're really in deep doo-doo.
There did not seem to be a half-way to me.
Astounding exercises, and also some are astoundingly hard.
