Abstract: Say we are "given" a set of matrices S, such that for any two matrices A and B from S, we have AB=BA. What kind of "structure" can we assume for the matrices in S?
It can be shown that for any such set S, there is a common basis under which every matrix in S will be _upper triangular_. One can also argue that there are sets of commuting matrices which are not simultaneously _diagonalisable_.
In the talk, we will first convince ourselves of the above two facts. We will then see a sufficient criterion, under which a set S of commuting matrices are simultaneously diagonalisable.
P.S.: I know the criterion from a work of Moller and Stetter (1995), but theirs is almost surely not the first work to observe this fact. Basic knowledge about polynomials and linear algebra will suffice to follow the talk.