Very good linear algebra book.?

Question

I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), linear maps and their matrix representation and eigenvectors and eigenvalues. I am looking for a book that handles every of the aforementioned topics in details. I also want to build a solid basis of the mathematical way of thinking to get ready to an exciting abstract algebra next semester, so my main aim is to work on proofs for somehow hard problems. I got Lang's "Intro. to Linear Algebra" and it is too easy, superficial. Can you advise me a good book for all of the above? Please take into consideration that it is for self-study, so that it' gotta work on its own. Thanks.

Answer 1

The book you need is Linear Algebra by Kenneth Hoffmann and Ray Kunze. This guys are from the MIT. I love this book, but is hard to understand in a first read. Even if you are familiar with the linear algebra concepts you say.

And intermediate reading between the Lang and the Hoffman-Kunze is the Linear Algebra by Seymour Lipschutz. It has an handy exposition of the theory with therorems and proofs easy to follow up and you won't frustrate if you read just the Hoffmann-Kunze.

My advice, keep both books together and read first the Lipschutz, then go to the Hoffmann-Kunze.

And for abstract algebra, My recommendation with closed eyes is the Abstract Algebra by Thomas Hungerford. The best book of abstract algebra ever written.