[nextos]

I guess baby Rudin (or Hubbard & Hubbard for something simpler) in the analysis department; and Halmos (or Axler) in the linear algebra department.

This is, essentially, Math 55. All 4 books have been used at different stages in this famous course.

[jhanschoo]

Halmos seems to discuss the same things as Hoffman and Kunze, which is the more “standard” and recommended book. Nevertheless after these you will still have to read up on multilinear algebra (tensors and determinant-like functions) as well as stuff on the numerical side of linear algebra.