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

2011/11/17 by Vanni Noferini, Noferini, Vanni
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1111.4004

openalex publication_date 2011/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)]^gP(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.

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