More Theoretical and Less Computational Linear Algebra Textbook
I don't really know the book you are talking about, so I can't give you an opinion on that. I suggest that you take a look at:
- Linear Algebra done Right - Sheldon Axler
I like the book of Hoffman & Kunze. It gives a very nice and quite rigorous treatment of linear algebra. The selection of problems is excellent.
I like Gilbert Strang's book, Introduction to Linear Algebra, but it may not be as advanced as some of the other suggestions here.
His video lectures are a useful companion to the book and a joy to watch.
I have always preferred Linear Algebra Done Wrong, a set of notes by Sergei Treil, over Axler's book, which, while being completely rigorous, is a practical introduction with a view to its applications.