Parameterized Structure-Preserving Transformations of Matrix Polynomials

Abstract

This paper examines the relationship between the companion forms of regular matrix polynomials with singular leading coefficients. When two such polynomials have the same underlying finite and infinite Jordan structures, it is shown that their companion forms are connected by a strict equivalence transformation that can be parameterized using the commutant of the companion forms' common Weierstrass canonical form. The process developed herein for generating such parameterized transformations is applied to the useful class of diagonalizable quadratic polynomials.