矩阵方程AXB=C存在自反解的条件及其通解表示  

The Conditions for Existence of Reflexive Solutions of Matrix Equation AXB=C and Its General Solution Representation

作　　者：邓勇 DENG Yong(College of Mathematics and Statistics, Kashgar University, Kashgar, Xininjiang, 844006, Chin)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844006

出　　处：《新疆师范大学学报（自然科学版）》2017年第3期57-60,共4页Journal of Xinjiang Normal University(Natural Sciences Edition)

摘　　要：对矩阵方程AXB=C关于反射矩阵的自反(反自反)解的讨论,通常借助的是矩阵分解、广义奇异值分解或共轭梯度法。为了更加有效和简洁地研究矩阵方程AXB=C的自反(反自反)解,利用矩阵的广义逆和广义反射矩阵给出了其存在自反解的充分必要条件。在有解的情况下,得到了其通解的一般表达式,并揭示出文献[1]的结果是该结果当B=I时的特例。The discussion of the reflexive （anti-reflexive） solutions of the matrix equation AXB=C with respect to the reflection matrix is usually utilize matrix decomposition, generalized singular value decomposition or conjugate gradient method. In order to study the reflexive （anti-reflexive） solutions of matrix equation AXB=C more effectively and concisely, the necessary and sufficient conditions for the existence of reflexive solutions are given by using the generalized inverse and generalized reflection of the matrix. In this ease, the general expression of its general solution is obtained and the result of the literature [1] is revealed as a special case when B=I.

关 键 词：自反矩阵 广义反射矩阵 矩阵方程 广义逆 

分 类 号：O151.21[理学—数学]