Graduate level linear algebra?

Question

Basically, I have a few related questions. The first one may seem a little naive, so please forgive me.

Is there much linear algebra to be taught beyond the level of books like Axler or Friedberg, Insel, and Spence? Is linear algebra typically taught beyond this advanced undergraduate/early graduate level, or would it just start to become abstract algebra and/or functional analysis?

If linear algebra is indeed taught at the graduate level, I would love some recommendations for some of the most commonly used textbooks.

I hope I phrased my question clearly and correctly, this is my first time posting here.

Answer 1

On the one hand, after linear algebra, which studies finite dimensional vector spaces, it is possible to study infinite dimensional vector spaces, however this is part of functional analysis:

1. Haim Brezis-Functional analysis, Sobolev spaces and partial differential equations.
2. Peter D. Lax-Functional analysis-Wiley (2002)

The second book (P. Lax) begins with a vector normed spaces and to my liking it is very constructive.

On the other hand, you can study linear algebra in more depth, seeing specific topics such as matrix analysis.

1. Carl D. Meyer-Matrix analysis and applied linear algebra. With solutions to problems-Society for Industrial and Applied Mathematics (2001).
2. Philip N. Klein-Coding the matrix. Linear algebra through computer science Applications-Newtonian Press (2013) (Especific topic)

In addition, linear algebra has important applications in optimization, where convex sets, polyhedra, etc. are studied. Or in the probability in discrete Markov chains