The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations

被引：14
作者：
Zhang, Yue [1 ]
Wang, Qing-Wen [1 ,2 ]
Xie, Lv-Ming [1 ]
机构：
[1] Shanghai Univ, Newtouch Ctr Math, Dept Math, Shanghai 200444, Peoples R China
[2] Collaborat Innovat Ctr Marine Artificial Intellige, Shanghai 200444, Peoples R China
来源：
SYMMETRY-BASEL | 2024年 / 16卷 / 03期
基金：
中国国家自然科学基金;
关键词：
commutative quaternion algebra; matrix equations; Hermitian matrix; least squares solution; SYLVESTER EQUATION; TRANSFORM;
D O I：
10.3390/sym16030361
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples.
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页数：14
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