Work

Row completion of polynomial and rational matrices

Year: 2025

Type: article

Abstract: We characterize the existence of a polynomial (rational) matrix when its eigenstructure (complete structural data) and some of its rows are prescribed. For polynomial matrices, this problem was solved in [1] when the polynomial matrix has the same degree as the prescribed submatrix. In that paper, the following row completion problems were also solved arising when the eigenstructure was partially prescribed, keeping the restriction on the degree: the eigenstructure but the row (column) minimal indices, and the finite and/or infinite structures. Here we remove the restriction on the degree, allowing it to be greater than or equal to that of the submatrix. We also generalize the results to rational matrices. Obviously, the results obtained hold for the corresponding column completion problems.

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2025.04.023

Authors: Agurtzane Amparan, Itziar Baragaña, Silvia Marcaida, Alicia Roca

Institutions: University of the Basque Country, Universitat Politècnica de València

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,230