Matrices over local rings
Linear algebra over a field have been studied for centuries. In many branches of math one
faces matrices over a ring, these came e.g. as "matrices of functions" or "matrices depending
on parameters". Linear algebra over a (commutative, associative) ring is infinitely more
complicated. Yet, some particular questions can be solved.
I will speak about two problems: block-diagonalization (block-diagonal reduction) of matrices
and stability of matrices under perturbations by higher-order-terms.