NIEP, SNIEP, RNIEP, and other problems in spectral nonnegative matrix theory
Date:
Abstract: Eigenvalues play a central role in linear algebra. For a given matrix, the process of finding these eigenvalues is straightforward. But what if, instead of a single matrix, I had a set of matrices? What shared behaviors do the corresponding eigenvalues have? Can we say where those eigenvalues are located? The talk will start with some background to known nonnegative matrix theory results and with an overview of some of the foundational questions in inverse eigenvalues problems. We will then discuss why we know these problems are solvable and what it would mean to solve them. Finally, I will end with some of my current ideas on approaching these problems.