Nov 18, 2022
Contact: Eric Swartz
Summary
{{ https://www.oldwestbury.edu/people/nicholas-werner, Nicholas Werner}} (SUNY Old Westbury)
Full Description
Title: Matrix Polynomials, Null Ideals, and Invertible Differences
Abstract: Given $k$ elements $a_1, ... , a_k$ from a field $F$, it is easy to find a polynomial with coefficients from $F$ that has $a_1, ... a_k$ as its roots. We will explore the analogous problem for matrices. That is, given $k$ matrices $A_1, ... , A_k$, all of size $n \times n$ and having entries from a field $F$, how can we find polynomials with matrix coefficients that have $A_1, ... , A_k$ as roots? Our focus will be on the cases where $n=2$ or 3. In these situations, our approach leads to the study of sets of similar matrices with the invertible difference property, which means that difference of any two distinct matrices from the set is invertible. Portions of this talk are joint work with Eric Swartz.
