On Characteristic Invariants of Matrix Pencils and Linear Relations

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-10-17 DOI:10.1137/22m1535449

H. Gernandt, F. Martínez Pería, F. Philipp, C. Trunk

引用次数: 1

Abstract

The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic and the Kronecker canonical form of the pencil. This relationship is exploited to obtain estimations on the invariant characteristics of matrix pencils under rank-one perturbations.

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矩阵铅笔的特征不变量与线性关系

研究了线性关系与矩阵铅笔的关系。给定一个线性关系，我们引入了它的Weyr特性。如果线性关系是给定矩阵铅笔的值域(或核)表示，我们证明了该特征与铅笔的Kronecker规范形式之间存在对应关系。利用这一关系得到了矩阵铅笔在秩一扰动下的不变特性的估计。

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

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.