数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 743-752.

• 论文 • 上一篇    下一篇

一四元数矩阵方程组的广义(反)反射解

张琴1, 王卿文1*, 常海霞2   

  1. 1. 上海大学数学系 上海 200444; 2. 上海金融学院 上海 201209
  • 收稿日期:2008-10-08 修回日期:2009-12-30 出版日期:2010-05-25 发布日期:2010-05-25
  • 通讯作者: wqw858@yahoo.com.cn E-mail:wqw858@yahoo.com.cn
  • 基金资助:

    国家自然科学基金(60672160)、上海市教委创新基金(09YZ13)和上海市教委重点学科建设项目(J50101)资助

The Generalized (Anti)reflexive Solutions to a System of Quaternion Matrix Equations

 ZHANG Qin1, WANG Qing-Wen1*, CHANG Hai-Xia2   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200444|2. Shanghai Finance University, Shanghai 201209
  • Received:2008-10-08 Revised:2009-12-30 Online:2010-05-25 Published:2010-05-25
  • Contact: wqw858@yahoo.com.cn E-mail:wqw858@yahoo.com.cn
  • Supported by:

    国家自然科学基金(60672160)、上海市教委创新基金(09YZ13)和上海市教委重点学科建设项目(J50101)资助

摘要:

该文给出了四元数矩阵方程组 X1B1=C1, X2B2=C2, A1X1B3+A2X2B4=Cb 可解的充要条件及其通解的表达式, 利用此结果建立了四元数矩阵方程组 XBa=Ca, AbXBb=Cb 有广义(反)反射解的充要条件及其有此种解时通解的表达式.

关键词: 四元数, 四元数矩阵, Moore-Penrose逆, 矩阵方程组, 广义反射矩阵

Abstract:

We give necessary and sufficient conditions for the existence of the general solution to the system of quaternion matrix equations  X1B1=C1, X2B2=C2, A1X1B3+A2X2B4=Cb . When the solvability conditions are met, we present an expression of the general solution to this system. Using the results on this system, we investigate necessary and sufficient conditions for the existence of generalized reflexive and generalized antireflexive solutions to the system of quaternion matrix equations XBa=Ca, AbXBb=Cb . We present expressions of the generalized reflexive and generalized antireflexive solutions to the system mentioned above when the solvability condtions are satisfied.

Key words: Quaternion, Quaternion matrix, Moore-Penrose inverse, System of matrix equations, Generalized reflexive matrix

中图分类号: 

  • 15A24