Research Seminar in Mathematics - Minimal Degenerations of Eigenstructure for Skew-Symmetric Matrix Polynomials

Speaker

Sweta Das, Örebro University.

Abstract

In this presentation, we describe qualitatively how eigenstructure of skew-symmetric matrix polynomials of odd degree changes under small perturbations in the matrix coefficients. Using strong linearization we prove a necessary and sufficient condition for one orbit of the linearization of a matrix polynomial to be a proper subset of the closure of the orbit of linearization of another polynomial. To achieve this, we introduce a set of rules describing structure transitions of the canonical blocks of the polynomial's linearization. These rules facilitate the construction of the stratification graphs of linearization of the polynomials. Finally, we state a method that allows us to sketch the entire or a part of the stratification graph of one matrix polynomial's linearization in relation to another matrix polynomial's linearization, provided both polynomials share the same degree but have different dimensions.

Welcome!