Direct methods on η-Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F)

被引：3

作者：

Li, Ming-Zhao ^{[1
]}

Yuan, Shi-Fang ^{[1
]}

Jiang, Hua ^{[1
]}

机构：

[1] Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 15期

关键词：

Kronecker product; matrix equation; split quaternion matrix;

D O I：

10.1002/mma.7273

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper provides two direct methods for solving the split quaternion matrix equation (AXB,CXD)=(E,F), where X is an unknown split quaternion eta-Hermitian matrix, and A, B, C, D, E, F are known split quaternion matrices with suitable size. Our tools are the Kronecker product, Moore-Penrose generalized inverse, real representation, and complex representation of split quaternion matrices. Our main work is to find the necessary and sufficient conditions for the existence of a solution of the matrix equation mentioned above, derive the explicit solution representation, and provide four numerical algorithms and two numerical examples.

引用

页码：15952 / 15971

页数：20

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