Good books to learn Linear Algebra? I took a course of Linear Algebra, but it was too basic (it only covered some elementary concepts of matrices and vectors). I am planning to purchase one of the three: Axler's Linear Algebra Done Right, Friedberg's Linear Algebra or Shilov's Linear Algebra. After one of those, I will read Hoffman's Linear Algebra, which I have learned is some advances Linear Algebra.
The topics I learned were the row echelon form, matrices operations, linear equations, inverse matrices, determinants, basic concepts of vectors, eigenvalues and eigenvectors. I want, however, to focus on the theory of it, rather than the applications (which is why I have not considered Strang's).
My Calculus course, however, has been very deep, so I consider myself able to learn proof-based mathematics books.
So, concluding, which of these three books would you recommend to me to read.
 A: I learned from Hoffman and Kunze and taught from Axler. Both are fine books. It might interest you to note that H&K was written for a course taken by sophomore math majors, and other interested parties, at MIT. The book is somewhat sophisticated, which is a testimony to the quality of MIT students. Nonetheless, if you are comfortable with proof based courses, it would not be unreasonable, even for a first go at linear algebra. You might even consider using H&K in conjunction with Axler, to get two different perspectives on the material.
A book which I always enjoyed was Halmos' "Finite Dimensional Vector Spaces." If you are near a college or university library, you might want to have a look at it. I thought it was available through Springer, but am not sure. It could be out of print.
A: I don't know the other books in detail, but I can really recommend Shilov. It is self-contained and thorough, and it's full of exercises, so quite good for self-study. It's also a Dover book, so it's affordable.
