English

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