I was looking for books in linear algebra and I came across a Math Stack exchange post explaining why the Linear Algebra book by Hoffman & Kunze is outdated. Is the book outdated or can it be considered an exaggeration ? Is Friedberg, Insel, and Spence equally or more rigorous and modern ? I was not able to find that post again and hence I am asking this as a separate question.
I am an undergrad and I have completed a course in Linear Algebra using Strang's Introduction to linear algebra and I was looking for a book on linear algebra that would be considered proof based and rigorous up to to the level of a strong undergrad. I want the book to possibly cover linear algebra in infinite dimensional fields and also over the complex field also (I guess quaternion and all would be there in M. Artin's book) I will be doing Abstract Algebra using M. Artin's Algebra book and Benedict Gross' lectures and I want to be done with Linear Algebra or at least until I take courses in Functional Analysis etc. I'm not using Sheldon Axler's book because it is less rigorous then Hoffman, doesnt include content on actualy finding the Jordan Form etc and it doesn't cover the complex field. I have also considered Halmos' book but that is even older and the title says Finite Dimensional and I would prefer one with infinite dimensions.
Any advice is appreciated
Edit: Changed sentence structure