ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX = BY AND XF-AX = BY

doi:10.1016/S0252-9602(12)60153-2

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1967-1982.doi: 10.1016/S0252-9602(12)60153-2

ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX = BY AND XF-AX = BY

宋彩芹|陈果良*|王晓东

1.Department of Mathematics, East China Normal University, Shanghai 200241, China；
2.School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

收稿日期:2010-12-31 修回日期:2012-02-20 出版日期:2012-09-20 发布日期:2012-09-20
通讯作者: CHEN Guan-Liang, glchen@math.ecnu.edu.cn E-mail:songcaiqin1983@163.com; glchen@math.ecnu.edu.cn；wangxiaodong2010@126.com
基金资助:
This project is granted financial support from NSFC (11071079), NSFC (10901056), Shanghai Science and Technology Commission Venus (11QA1402200), Ningbo Natural Science Foundation (2010A610097), the Fundamental Research Funds for the Central Universi-
ties and Zhejiang Natural Science Foundation (Y6110043).

ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF -AX = BY AND XF-AX = BY

SONG Cai-Qin, CHEN Guan-Liang*, WANG Xiao-Dong

陈果良|glchen@math.ecnu.edu.cn

Received:2010-12-31 Revised:2012-02-20 Online:2012-09-20 Published:2012-09-20
Supported by:
This project is granted financial support from NSFC (11071079), NSFC (10901056), Shanghai Science and Technology Commission Venus (11QA1402200), Ningbo Natural Science Foundation (2010A610097), the Fundamental Research Funds for the Central Universi-
ties and Zhejiang Natural Science Foundation (Y6110043).

摘要/Abstract

摘要：

In this paper, the quaternion matrix equations XF − AX = BY and XF −AX= BY are investigated. For convenience, they were called generalized Sylvester-quaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equa-tion, which include the Sylvester matrix equation and Lyapunov matrix equation as special cases. By applying of Kronecker map and complex representation of a quaternion matrix, the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF − AX = BY and XF − AX = BY are also obtained. By the established expressions, it is easy to compute
the solution of the quaternion matrix equation in the above two forms. In addition, two practical algorithms for these two quaternion matrix equations are give. One is complex representation matrix method and the other is a direct algorithm by the given expression. Furthermore, two illustrative examples are proposed to show the efficiency of the given method.

关键词: Kronecker map, explicit solution, generalized Sylvester-quaternion matrix equation, complex representation method

Abstract:

Key words: Kronecker map, explicit solution, generalized Sylvester-quaternion matrix equation, complex representation method

中图分类号:

15A06

宋彩芹, 陈果良, 王晓东. ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX = BY AND XF-AX = BY[J]. 数学物理学报(英文版), 2012, 32(5): 1967-1982.

SONG Cai-Qin, CHEN Guan-Liang, WANG Xiao-Dong. ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF -AX = BY AND XF-AX = BY[J]. Acta mathematica scientia,Series B, 2012, 32(5): 1967-1982.

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ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX = BY AND XF-AX = BY

ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF -AX = BY AND XF-AX = BY

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