Linear Algebra Good reading on Applied Linear Algebra?

[CSteiner]

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.

 

[S.G. Janssens]

For a feel of what I'm dealing with, here is the table of contents:

This is part of the table of contents, correct? Are these the subjects that you would particularly like to see applications of?

I have more than once contemplated buying and studying (parts of) this book. So far I have decided against it because it is a bit too algebraic for me and (as you also remarked) it seems to lack applications, but maybe I will change my mind.

Would Matrices: Algebra, Analysis and Applications by S. Friedland be something for you, or is that too much towards matrix theory for your tastes?

 

[CSteiner]

This is part of the table of contents, correct? Are these the subjects that you would particularly like to see applications of?

Yes, this is the first half of the book, and these are the subjects I'd like to see some examples of.

Would Matrices: Algebra, Analysis and Applications by S. Friedland be something for you, or is that too much towards matrix theory for your tastes?

I may try this, the applications to graph theory look promising. To be honest though, this seems more like an equivalently abstract formulation of the subject in terms of matrices. I'm more looking for specific instances of the concepts in physics and other areas of math.