二次广义Hermite矩阵方程的解

J4 ›› 2012, Vol. 50 ›› Issue (02): 281-283.

二次广义Hermite矩阵方程的解

袁晖坪

重庆工商大学数学与统计学院, 重庆 400067

收稿日期:2011-08-22 出版日期:2012-03-26 发布日期:2012-03-21
通讯作者: 袁晖坪 E-mail:yhp@ctbu.edu.cn

Solutions of Quadratic Generalized Hermite Matrix Equation

YUAN Huiping

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received:2011-08-22 Online:2012-03-26 Published:2012-03-21
Contact: YUAN Huiping E-mail:yhp@ctbu.edu.cn

摘要/Abstract

摘要：

利用广义Hermite矩阵探讨一类二次矩阵方程的求解问题, 得到了矩阵方程XAX=A存在广义Hermite矩阵解的充分必要条件及其相应解的表达式, 并给出了矩阵方程XAY=B当A,B可逆时的通解表达式.

关键词: 广义Hermite矩阵；二次矩阵方程；矩阵解；通解

Abstract:

The solutions of quadratic matrix equation were discussed via the generalized Hermite matrix. The findings show that there are necessary and sufficient conditions of matrix equation XAX=A having their generalized Hermite matrix solution, and the simple expressions of the generalized Hermite matrix solution can also be obtained. Besides, the general solutions of the matrix equations XAY=B were given.

Key words: generalized Hermite matrix, quadratic matrix equation, matrix solution, general solution

中图分类号:

O151.21

袁晖坪. 二次广义Hermite矩阵方程的解[J]. J4, 2012, 50(02): 281-283.

YUAN Hui-Ping. Solutions of Quadratic Generalized Hermite Matrix Equation[J]. J4, 2012, 50(02): 281-283.

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