| 一四元数矩阵方程组的广义(反)反射解 |
| |
| 引用本文： | 张琴,王卿文,常海霞.一四元数矩阵方程组的广义(反)反射解[J].数学物理学报(A辑),2010,30(3):743-752. |
| |
| 作者姓名： | 张琴 王卿文 常海霞 |
| |
| 作者单位： | 张琴,王卿文(上海大学数学系,上海,200444);常海霞(上海金融学院,上海,201209) |
| |
| 基金项目： | 国家自然科学基金，上海市教委创新基金，上海市教委重点学科建设项目 |
| |
| 摘 要： | 该文给出了四元数矩阵方程组X_1B_1=C_1,X_2B_2=C2,A_1X_1B_3+A_2X_2B_4=C_b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XB_a=C_a,A_bXB_b=C_b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 |
| 收稿时间： | 2008-10-08 |
| 修稿时间： | 2009-12-30 |
The Generalized (Anti)reflexive Solutions to a System of Quaternion Matrix Equations |
| |
| ZHANG Qin,WANG Qing-Wen,CHANG Hai-Xia.The Generalized (Anti)reflexive Solutions to a System of Quaternion Matrix Equations[J].Acta Mathematica Scientia,2010,30(3):743-752. |
| |
| Authors: | ZHANG Qin WANG Qing-Wen CHANG Hai-Xia |
| |
| Institution: | 1. Department of Mathematics, Shanghai University, Shanghai 200444|2. Shanghai Finance University, Shanghai 201209 |
| |
| 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. |
| |
| Keywords: | Quaternionzz Quaternion matrixzz Moore-Penrose inversezz System of matrix equationszz Generalized reflexive matrixzz |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《数学物理学报(A辑)》浏览原始摘要信息 |
| 点击此处可从《数学物理学报(A辑)》下载免费的PDF全文 |
