Row completion of polynomial and rational matrices

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-06 DOI:10.1016/j.laa.2025.04.023

Agurtzane Amparan , Itziar Baragaña , Silvia Marcaida , Alicia Roca

引用次数: 0

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.

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多项式和有理矩阵的行补全

当一个多项式（有理）矩阵的特征结构（完全结构数据）和它的一些行被规定时，我们刻画了它的存在性。对于多项式矩阵，当多项式矩阵与规定的子矩阵具有相同的次时，该问题在[1]中得到解决。本文还解决了在保留程度限制的情况下部分规定特征结构时出现的下述行补全问题：特征结构只有行（列）最小指标，有限和/或无限结构。这里我们去掉了度数的限制，允许它大于或等于子矩阵的度数。我们也将结果推广到有理矩阵。显然，所得结果适用于相应的列补全问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.