I am currently a first year graduate student in math, and I am trying to pick a linear algebra book to work through during the winter break. I have already gone through the computational style linear algebra, and I have also gone through Axler's Linear Algebra Done Right. I would like to go through a more advanced LA text, and I have been considering two choices: Halmos' Finite Dimensional Vector Spaces and Steven Roman's Advanced Linear Algebra. Roman's looks like it covers more material, and also covers modules and PIDs which would be a welcome review from my Abstract Algebra class this fall. Halmos is, however, a classic, and I'm not sure which would be more appropriate for my eventual goals in differential geometry - both cover the tensor product, although I think perhaps Roman's book does more with it. There's also Hoffman and Kunze, but I looked over the table of contents and didn't see anything I hadn't already covered. Any suggestions?