I've taken a course in linear algebra a couple years ago, but I didn't take away too much from it, and now I'm looking to take some higher level math courses and have been brushing up on the subject, spending about an hour to two hours a day going through my old notes and textbook. However, the class I took wasn't very proof driven, and was more computational. We didn't get down to much of the theory behind the subject. I don't feel like taking another linear algebra course and would rather just learn the subject the best I can on my own. Any recommendations of books or other methods that would really give me a good insight into the subject? Also, as far as pure math is concerned, in which other areas of study does the knowledge of linear algebra become most useful?, i.e. analysis, topology, etc. Not sure if this is relevant, but this fall I'll be taking a course in abstract algebra and an introduction to analysis.