Here are some notes to a few of the sections in Strang's Introduction to Linear Algebra
These are some notes to the beginning of Axler's paper Down with Determinants. There are also some notes on diagonalization and the Jordan canonical form that I covered, in conjunction with the paper.
These are some notes I wrote up when reading through Fuhrmann's A Polynomial Approach to Linear Algebra. As I noted in the literature review, the approach in this book is unique.