I am looking for a sucint and complete book of Matrix theory, in the style properties/theorems enunciations and it's proof.
The topics that are a must to me it's the following (they may not be quite related):
1)properties of symmetric matrices, traces, eigenvalues, eigenvectors (left and right), etc.
2)definites matrices (positive, negative, semidefinites, and all it's properties)
3) quadratic forms
4) SVD , cholesky decompositions
5) schur complement, pseudoinverse
6) Matrix/vectors norms and condition numbers
7) QR factorization
The ideal approach for me is a book that focus on enunciation of a LOT of properties/theorems and it's proofs (not bothering with applications or computations examples) and it's "separate" from linear algebra (the book only gives the minimum, I dont want to go deep on vector spaces and linear transformations for example). In short, I want to know a lot of properties /theorems (and its proofs) regarding the topics I wrote without spending too much time for it.
Also, I took a look at Matrix Analysis book by Horn and Johnson and seems to me that it does not covers all the topics that I wrote, not to mention it's quite large (600 pages). Since I am studying and working on other things, 600 pages are a lot to me. About 300 pages would be ok.
If you guys think my requirements are too much, you could give suggestions like "this book for this topic, this one for this.. etc".
obs: I'm not interested on complex matrix theory right now.
So that's it, thank you for your time =)