The list of martix algebra textbooks is very large. Go to http://gen.lib.rus.ec/ and search under MATRIX THEORY, and MATRICES. Besides many others, you can download the following:
1.- Richard Bronson. Schaum's Outline of Theory and Problems of Matrix Operations
2.- Kwong-Tin Tang. Determinants and Matrices
3.- Mitrinovic D.S. Elementary matrices
4.- Gantmacher F.R. The Theory of Matrices
5.- Howard Eves Elementary Matrix Theory
After browsing these digital texts you can decide about borrowing a hardcopy from your institute library, or about buying it.
If you need to know basic matrix theory, try Matrix theory by David Lewis. If you want to do a full course on it, Matrix Analysis by Horn and Johnson will suffice.
I recommend you "Matrix Analysis" and "Topics in Matrix Analysis" of Horn and Johnson (these are classics in Matrix Analysis).
Other books that I used for Mathematical theory of Control are: (1) Gantmacher, Felix (1959), Theory of matrices, AMS Chelsea publishing, (2) Gantmacher, Felix (1959), Applications of the theory of matrices, Interscience publishers.
I like very much the series "Classics in Applied Mathematics" of SIAM which includes monographs (of high level and very useful) such as "Matrix Polynomials", "Introduction to Matrix Analysis", "Nonnegative in the Mathematical Sciences", et cetera.
Definitely if I were you I should take a look SIAM's books.