关于矩阵方程AXB=C的广义Hermitian非负定解  

A generalized Hermitian nonnegative-definite solution on matrix equation AXB=C

作　　者：邓勇 DENG Yong(College of Mathematics and Statistics,Kashi University,Kashi 844006,China)

机构地区：[1]喀什大学数学与统计学院

出　　处：《东北师大学报（自然科学版）》2019年第3期10-14,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：新疆维吾尔自治区自然科学基金资助项目(2016D01A014)

摘　　要：给出了矩阵方程AXB=C存在广义Hermitian非负定解的一个充要条件,推导出了其表达式,并将此结果应用到两个实例上.通过比较新旧两种方法得出的广义Hermitian非负定解,指出了已有结果的错误性.同时给出了两个矩阵二次型随机独立的一般协方差结构.In this paper,a sufficient and necessary condition for the existence of generalized Hermitian nonnegative definite solution of matrix equation AXB = C is given,and its expression is derived. This result is applied to two instances. Compared with the generalized Hermitian nonnegative definite solution that obtained by this paper and a literature,It is found that the solution given in the literature is wrong. Meanwhile, general covariance structure of two matrix quadratic random independent was given.

关 键 词：矩阵方程 广义逆矩阵 平行可加矩阵 对称系统 

分 类 号：O152[理学—数学]