Looking for a recommendation on theory of linear operator decompositions.
I know some basics of linear algebra: what is a vector space, what is a linear operator, how to compute eigenvalues/eigenvectors of a matrix, etc.
What I’m interested in (and find missing in the books I have) is how all the various decompositions work (SVD, Jordan form, etc) and — most importantly — what do they tell about the properties of a given linear operator.
This is not a “practical” question — i.e. I’m not just looking for “how to perform SVD decommission” or “most effective numerical method to compute eigenvalues”, but rather “why would I want to do it? What can I learn from it about the structure of the operator?”
I’d prefer a book with more illustrations and examples rather than “theorem-and-proof”-style (I have enough theory to learn already, ha-ha).
Thanks!