I am trying to learn both linear and abstract algebra. I already took a basic Matrix Theory course using Anton's linear algebra book (not very rigorous) and I want to self study the rest of the subject. We got to basic eigen values and eigen spaces. I want to relearn linear algebra rigorously, and I am considering Hoffman and Kunze. I have a good background in rigor, and am reading Rudin's Principles of Mathematical Analysis, so I think I would be able to handle Hoffman and Kunze.
However, I also want to learn abstract algebra. My question is, do abstract algebra books, say like Dummit and Foote cover everything in a linear algebra book like Hoffman and Kunze? Or would I have to read them simultaneously?