I'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.