Row or column completion of polynomial matrices of given degree

2023/04/08 by A. Amparan, Itziar Baragaña, Amparan, A. +5 · 2 citations
Computer Science · Engineering · Mathematics · #15A18 #15A54 #15A83 #93B18 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2306.06104

openalex publication_date 2023/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column) completion problem of a polynomial matrix of given degree under different prescribed invariants: the whole eigenstructure, all of it but the row (column) minimal indices, and the finite and/or infinite structures. Moreover, we characterize the existence of a polynomial matrix with prescribed degree and eigenstructure over an arbitrary field.

Cited by

• Row completion of polynomial and rational matrices II
• Bounds for the change of the Weyr characteristic of matrix pencils after 1-rank perturbations
• Polynomial and rational matrices with the invariant rational functions and the four sequences of minimal indices prescribed

Related

• Row or column completion of polynomial matrices of given degree II
• Row completion of polynomial and rational matrices
• Row completion of polynomial and rational matrices II
• The behaviour of the complete eigenstructure of a polynomial matrix under a generic rational transformation
• Polynomial and rational matrices with the invariant rational functions and the four sequences of minimal indices prescribed