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
收藏
页码：2731 / 2742
页数：12
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