四元数矩阵方程AXB+CXD=E的广义延拓解  

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

作　　者：蓝家新 黄敬频 毛利影 王敏 Lan Jiaxin;Huang Jingpin;Mao Liying;Wang Min(College of Science,Guangxi University for Nationalities,Nanning 530006,China)

机构地区：[1]广西民族大学理学院,南宁530006

出　　处：《计算数学》2020年第4期497-507,共11页Mathematica Numerica Sinica

基　　金：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.

摘　　要：本文在四元数体上讨论矩阵方程AXB+CXD=E的广义行(列)共轭延拓解问题.利用四元数矩阵的复与实分解,以及广义共轭延拓矩阵的结构特点,借助矩阵Kronecker积,把约束四元数矩阵方程转化为实数域上无约束方程,从而得到该方程具有广义行(列)共轭延拓解的充要条件及其通解表达式.最后通过数值算例说明所给算法的可行性.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.

关 键 词：四元数体 矩阵方程 共轭延拓矩阵 KRONECKER积 MOORE-PENROSE广义逆 

分 类 号：O151.21[理学—数学]