The reducible solution to a system of matrix equations over the Hamilton quaternion algebra

被引：6

作者：

Liu, Long-Sheng ^{[1
]}

Wang, Qing-Wen ^{[1
,2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Collaborat Innovat Ctr Marine Artificial Intellige, Shanghai 200444, Peoples R China

来源：

FILOMAT | 2023年 / 37卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Matrix equation; Hamiltion quaternion; Reducible matrix; Moore-Penrose inverse; Rank; LEAST-SQUARES SOLUTIONS; GENERALIZED REFLEXIVE; AX; XC;

D O I：

10.2298/FIL2309731L

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Reducible matrices are closely associated with the connection of directed graph and can be used in stochastic processes, biology and others. In this paper, we investigate the reducible solution to a system of matrix equations over the Hamilton quaternion algebra. We establish the necessary and sufficient conditions for the system to have a reducible solution and derive a formula of the general reducible solution of the system when it is solvable. Finally, we present a numerical example to illustrate the main results of this paper.

引用

页码：2731 / 2742

页数：12

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