A Classical System of Matrix Equations Over the Split Quaternion Algebra

被引：3

作者：

Si, Kai-Wen ^{[1
,2
]}

Wang, Qing-Wen ^{[3
,4
]}

Xie, Lv-Ming ^{[3
,4
]}

机构：

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

[2] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China

[3] Shanghai Univ, Collaborat Innovat Ctr Marine Artificial Intellige, Dept Math, Shanghai 200444, Peoples R China

[4] Shanghai Univ, Newtouch Ctr Math, Collaborat Innovat Ctr Marine Artificial Intellige, Shanghai 200444, Peoples R China

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2024年 / 34卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Split quaternion matrix equations; Real representation; General solution; ANTI-REFLEXIVE SOLUTIONS; HERMITIAN SOLUTION; AX; ROTATIONS; XC;

D O I：

10.1007/s00006-024-01348-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We design several real representations of split quaternion matrices with the primary objective of establishing both necessary and sufficient conditions for the existence of solutions within a system of split quaternion matrix equations. This includes conditions for the general solution without any constraints, as well as X = +/- X solutions and eta-(anti-)Hermitian solutions. Furthermore, we derive the expressions for the general solutions when it is solvable. As an application, we investigate the solutions to a system of five split quaternion matrix equations involving X*. Finally, we present several algorithms and numerical examples to demonstrate the results of this paper.

引用

页数：34

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