I've looked through a few linear algebra books, I studied most of the Horner book and found it good but it got a little hairy - Hermitian forms, etc, although necessary for my subject (engineering) its not enjoyable. I like Gilbert Strang's course, he teaches the basics well. I've got his book and I find some of the problems very difficult. My plan is to study that book and do the easier problems to get a handle on things then get into pure math with an intro to proofs as I have never been good with proofs. I am good with difficult problems, but I never got the knack of proving things well in math. Fortunately you don't have to do much of this in engineering. I got my degree twenty years ago and now see that engineering is done with linear algebra rather than calculus. Fortunately I know my DSP quite well.I'm curious about a good pure math book myself, to start doing proofs - calc or algebra - just a good book for self study.