The behaviour of the complete eigenstructure of a polynomial matrix under a generic rational transformation

Abstract

Given a polynomial matrix P(x) of grade g and a rational function $x(y)=n(y)/d(y)$, where $n(y)$ and $d(y)$ are coprime nonzero scalar polynomials, the polynomial matrix $Q(y):=[d(y){]}^{g}P(x(y))$ is defined. The complete eigenstructures of $P(x)$ and $Q(y)$ are related, including characteristic values, elementary divisors and minimal indices. A Theorem on the matter, valid in the most general hypotheses, is stated and proved.

Submitted

Cited by in corpus (1)

• Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method