I have heard that Peter Lax's linear algebra book is the hardest you can find on the subject, but that it is the greatest linear algebra text in the world. But I also hear great things about Gil Strang's book.
How do I go about choosing between the two?
Here's an idea in my mind:
Choose Strang if I'm headed towards engineering mathematics, else choose Lax if I'm headed towards more theoretical, say, functional analysis.