• 论文 •

### 四元数矩阵方程AXB+CXD=E的广义延拓解

1. 广西民族大学理学院, 南宁 530006
• 收稿日期:2019-01-25 出版日期:2020-11-15 发布日期:2020-11-15
• 通讯作者: 黄敬频,Email:hjp2990@126.com.
• 基金资助:

国家自然科学基金项目（11661011）；广西民族大学研究生创新项目（gxun-chxzs2017142）资助.

Lan Jiaxin, Huang Jingpin, Mao Liying, Wang Min. THE CONJUGATED EXTENDED MATRIX SOLUTIONS OF THE QUATERNION EQUATION AXB + CXD=E[J]. Mathematica Numerica Sinica, 2020, 42(4): 497-507.

### THE CONJUGATED EXTENDED MATRIX SOLUTIONS OF THE QUATERNION EQUATION AXB + CXD=E

Lan Jiaxin, Huang Jingpin, Mao Liying, Wang Min

1. College of Science, Guangxi University for Nationalities, Nanning 530006, China
• Received:2019-01-25 Online:2020-11-15 Published:2020-11-15

This paper is aimed at discussing the column and row conjugated extended matrix solutions of quaternion equation AXB + CXD = E. By using the complex and real decomposition of a quaternion matrix, the Kronecker product of matrices and the specific structure of a conjugated extended matrix, the quaternion equation with constraints can be converted to an unconstrained equation. Then the necessary and sufficient condition for the existence of the quaternion matrix equation AXB + CXD = E with column and row conjugated extended matrix and their general solution expression are obtained. Finally, the feasibility of the proposed algorithm will be illustrated through the numerical example.

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