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?
Best Answer
No there is not enough Linear algebra in an Abstract algebra book. But I have a really good suggestion for you. But that will eat up at least two months of your time but will get you crystal clear understanding of Algebras.
Give at least 20 days to the book (if you have never been introduced to this subject before, then may be at least 30 days) Volume 1: Groups.
Then give 20 - 30 days atleast to Volume 2: Rings
Then Finally you can start with Linear algebra- (which is nothing but study of modules over fields). Read at whatever pace you like, as it is a gem of a book Volume 3: Modules
Then if you feel like, you can finish up the series with Volume 4:Field Theory.
I hope it helps.