I just recently finally bought Strang's introduction to Linear Algebra. The book itself is very dense and, dare I say, scary to a newcomer, but his videos are amazingly clear in combination with the book.

I am in the beginning, but so far, I'd recommend the book. Though, the steep price (almost 100USD over here) makes it a bit difficult to recommend. I might buy Boyd’s and Vandenberghe’s Introduction to Applied Linear Algebra later and write a comparison.