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.