A great resource that isn't mentioned often is the linear algebra chapters in Birkhoff and Mac Lane's Survey of Modern Algebra. Chapters 7,8,9, and 10 (in the 4th and 5th editions anyway) are a self-contained book-within-a-book of about 200 pages on both the computational and theoretical aspects of vector spaces, matrices, linear transformations, and determinants.

Many times I've been puzzled by a concept just to go there and find it made simple and obvious. It's a real golden nuggett... Plus if you then want to go further into groups, rings, fields, and Galois theory, that's also there.