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arXiv · 2306.06104

Row or column completion of polynomial matrices of given degree

A. Amparan·I. Baragaña·S. Marcaida·A. Roca
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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.

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A. Amparan, I. Baragaña, S. Marcaida, A. Roca. 2023-04-08. Row or column completion of polynomial matrices of given degree. https://arxiv.org/abs/2306.06104

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