Row or column completion of polynomial matrices of given degree
Rings and Algebras
2024-02-07 v2
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.
Keywords
Cite
@article{arxiv.2306.06104,
title = {Row or column completion of polynomial matrices of given degree},
author = {A. Amparan and I. Baragaña and S. Marcaida and A. Roca},
journal= {arXiv preprint arXiv:2306.06104},
year = {2024}
}
Comments
22 pages, research paper