CSteiner

ve been studying graduate level Linear Algebra from Steven Roman's Advanced Linear Algebra (Springer, GTM). It is a terrific book, but many of the concepts are extremely abstract so that I find it difficult to retain what I've learned. Can anyone point me to some books/reading on the applications of abstract Linear Algebra to other fields of Math, or physics? Note that I am not referring to the low level matrix manipulation approach taught in undergrad, but the more heavy ideas. For a feel of what I'm dealing with, here is the table of contents:

1.Vector Spaces
2. Linear Transformations
3.The Isomorphism Theorems
4.Modules I:Basic Properties
5. Modules II: Free and Noetherian Modules
6. Modules over a Principle ideal Domain
7. The Structure of a Linear Operator
8. Eigenvalues and Eigenvectors
9. Real and Complex innerprodict spaces
10. Structure Theory for Normal Operators.

SDK

https://www.amazon.com/Linear-Algebr.../dp/0030105676
it doesn't get better than this.