As an undergrad, I studied linear algebra from Hoffman and Kunze. It was a good book and it covers some of the stuff I care about, but I'm wondering if there are better resources. The topics I would like to revisit (and primarily from a matrix pov) are matrix decompositions, normal forms, spectral theorems, variational characterization of eigenvalues, and some special well behaved matrices (graph matrices/doubly stochastic matrices). Different resources seem to address different topics really well, and I've picked some stuff up from Bhatia, Trefethan-Bau, Spielman's notes on spectral graph theory, but are there books that address all/most of these topics? There's a few books I came across, which I list below, but I would be glad to hear more suggestions (hopefully with some detail so that it becomes easier to pick a book).
- Advanced Linear Algebra: S Roman (greatest overlap so far, but possibly not very matrix centric)
- Advanced Linear and Matrix Algebra: Nathaniel Johnston (this came out earlier this month)
- Linear Algebra and Optimization for Machine Learning: Charu Aggarwal (my interest is not from an ML point of view, so apprehensive that this might go down a different path)