Having gone through most of howard anton and chris rorres elementary linear algebra at my school. We have gone through some proofs, but the main focus was how to turn problems into matrices and then compute. We covered Vector spaces, determinants, linear transformations, diagonalization eigenvectors and inner products. Im interestes in having a stronger background in linear algebra. Especially in terms of proofs in vector spaces and linear mappings, could someone suggest a book for this?