给定度数多项式矩阵的行或列补全

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-07 DOI:10.1137/23m1564547

Agurtzane Amparan, Itziar Baragaña, Silvia Marcaida, Alicia Roca

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引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 478-503 页，2024 年 3 月。摘要我们解决了当一个固定阶数的多项式矩阵的特征结构（或部分特征结构）及其部分行（列）被规定时，该矩阵的存在性问题。更具体地说，我们提出了给定度数的多项式矩阵在不同规定不变式下行（列）补全问题的解决方案：整个特征结构、除行（列）最小索引外的所有特征结构以及有限和/或无限结构。此外，我们还描述了任意域上具有规定度和特征结构的多项式矩阵的存在性。

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Row or Column Completion of Polynomial Matrices of Given Degree

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 478-503, March 2024.
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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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.