I am an advanced undergrad in computer science/statistics. Is there a linear algebra textbook that covers determinants, eigenvalues&eigenvectors, transpose, vector spaces, etc.. and tries to proof them? I have an applied book, and would like a theory based one. The other threads are over 6-9+ years old and I just wanted to see if any more recent texts have come out since.
A great example of what i'm looking for can be found in Casella&Berger's classic textbook on theoretical statistics, Statistical Inference, where they attempt to teach Stats through slowly building a toolbox starting with axioms and then forming theorems from them.
I am a big fan of starting small and building big in textbooks. At first, I thought Axler would be the right approach, but considering how hard some of the older threads came down on the book, I may as well ask for mroe suggestions.