Vector space of linearizations for the quadratic two-parameter matrix polynomial

TL;DR

This paper introduces a systematic method to generate a vector space of linearizations for quadratic two-parameter matrix polynomials, aiding in solving related eigenvalue problems.

Contribution

It develops a systematic approach to generate and identify linearizations within a vector space for quadratic two-parameter matrix polynomials.

Findings

Identifies a set of linearizations within the vector space.

Determines a class of linearizations for quadratic two-parameter eigenvalue problems.

Abstract

Given a quadratic two-parameter matrix polynomial Q, we develop a systematic approach to generating a vector space of linear two-parameter matrix polynomials. We identify a set of linearizations of Q that lie in the vector space. Finally, we determine a class of linearizations for a quadratic two- parameter eigenvalue problem.