These notes may be too condensed to be of use to you but they are free. The first 3 pages of text give a complete summary of the whole elementary theory of linear transformations and their canonical forms, such as Jordan and rational canonical form, plus the basic spectral theorems. Those 3 pages are necessarily quite dense since they sumamrize the content of books of some 300-400 pages, but you might benefit from reading them several times. In particular they make the observation, not always made clear in books, that diagonalizing matrices, although handy theoretically, is usually not feasible in practice, even in cases where it is theoretically possible. In particular the step of factorizing the characteristic polynomial, in the process of attempted diagonalization, is not actually feasible for most matrices. The moral is that for many applied purposes, methods of approximation should be learned as well. Those methods are not treated here however in this more theoretical essay. However, it is made clear exactly which calculations are feasible "by hand", and which ones are not. E.g. it is quite feasible to compute both the characteristic and minimal polynomials for any matrix, as well as the invariant factors and the rational canonical form, although not the Jordan [or diagonal] form in general.
http://alpha.math.uga.edu/%7Eroy/laprimexp.pdf
as far as recommendations go, I second most of Buffu's suggestions, especially Sergei Treil's LA Done wrong.
