矩阵方程AXB+CXTD=E的可解性

J4 ›› 2012, Vol. 47 ›› Issue (10): 45-48.

矩阵方程AXB+CXTD=E的可解性

赵琳琳

德州学院数学系,山东德州 253023

收稿日期:2011-08-08 出版日期:2012-11-20 发布日期:2012-10-26
作者简介:赵琳琳(1981- ),女,博士,研究方向为数值代数.Email:zhaolinlin0635@163.com
基金资助:
国家自然科学基金资助项目(11071079;10971070);德州学院人才引进项目(12RC05)

Solvability of the matrix equation AXB+CXTD=E

ZHAO Lin-lin

Department of Mathematics, Dezhou University, Dezhou 253023, Shandong, China

Received:2011-08-08 Online:2012-11-20 Published:2012-10-26

摘要/Abstract

摘要：

利用矩阵的广义逆研究了矩阵方程AXB+CXTD=E的可解性, 得到了若干可解的条件以及解的一般表达式。

关键词: 矩阵方程;可解;对称矩阵;斜对称矩阵

Abstract:

The problem for the solvability of the matrix equation AXB+CXTD=E is considered by using the Moore—Penrose generalized inverse of the matrix. Some solvability conditions and a general solution to this equation are obtained.

Key words: matrix equation; solvability; symmetric matrix; skew-symmetric matrix

赵琳琳. 矩阵方程AXB+CXTD=E的可解性[J]. J4, 2012, 47(10): 45-48.

ZHAO Lin-lin. Solvability of the matrix equation AXB+CXTD=E[J]. J4, 2012, 47(10): 45-48.

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