Suggestion for a book on Linear Algebra Please suggest a Linear Algebra book with an introduction and rigorous theory (description) on Eigenvectors , eigen-values , Cayley-Hamilton theorem , Diagonalisation of matrices ; Quadratic forms ( Sylvester's Law , rank , signature , reduction to canonical forms ) . 
Thanks in advance 
 A: I suggest Linear Algebra by Serge Lang. I studied those arguments using that book and it's excellent. 
A: I suggest Linear Algebra by Hoffman and Kunze which covers those topics and have some excellent exercises 
A: A very good first course (for mathematically solid students) is Sergei Treil's "Linear Algebra Done Wrong." There is a reason for the odd name, described in the link. Here is the text. Best of all: IT'S FREE!
If you have seen some linear algebra, and you want an introduction to the coordinate-free approach, check out this (ALSO FREE!) cool book by Sergei Winitzki called "Linear Algebra via Exterior Products." You'll likely find it challenging, but it's worth the trouble.
A: I think these are some well written and helpful books on the subjects you mentioned:


*

*Basic Linear Algebra - Blyth, Robertson

*Further Linear Algebra - Blyth, Robertson

*Matrix Analysis and Applied Linear Algebra - Meyer
All of them provide solutions to every single problem they present, so they're particularly appropriate for self-study.
The first two, by Blyth and Robertson, are a little bit more compact while the book by Meyer feels more like a bible; that being said, Meyer's book has lots of solved examples and applications to motivate the theory and, in my opinion, it is still quite strong on the theoretical side.
