广义对称约束条件下矩阵表达式A-BXC 的极秩问题

doi:10.6040/j.issn.1671-9352.0.2014.227

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (02): 90-94.doi: 10.6040/j.issn.1671-9352.0.2014.227

• 论文 • 上一篇

广义对称约束条件下矩阵表达式A-BXC 的极秩问题

代丽芳, 梁茂林, 何万生

天水师范学院数学与统计学院, 甘肃天水 741001

收稿日期:2014-05-16 修回日期:2014-10-15 出版日期:2015-02-20 发布日期:2015-01-27
通讯作者: 梁茂林(1981-),男,硕士,讲师,研究方向为数值线性代数. E-mail:liangml2005@163.com E-mail:liangml2005@163.com
作者简介:代丽芳(1981-),女,硕士,讲师,研究方向为非线性泛函分析. E-mail:dailf2005@163.com
基金资助:
甘肃省教育厅项目(1108B-03);天水师范学院青年基金项目(TSA1315)

The minimal and maximal ranks problems of matrix expression A-BXC under generalized symmetric constraints

DAI Li-fang, LIANG Mao-lin, HE Wan-sheng

School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, Gansu, China

Received:2014-05-16 Revised:2014-10-15 Online:2015-02-20 Published:2015-01-27

摘要/Abstract

摘要： 给定R,S为广义自反矩阵,即R^*=R, R²=I, S^*=S, S²=I,若矩阵X满足RXS=X(RXS=-X),则称之为广义反射矩阵(广义斜反射矩阵).当变量矩阵X为广义反射矩阵或广义斜反射矩阵时,讨论了矩阵表达式A-BXC的极秩问题,并得到了矩阵方程BXC=A的一些可解性条件.

关键词: 广义自反矩阵, 广义反射矩阵矩阵, 矩阵方程, 广义斜反射矩阵, 极大极小秩

Abstract: Let R,S be generalized reflection matrices, that is, R^*=R, R²=I, S^*=S, S²=I. A matrix X is called generalized reflective matrix (generalized skew-reflective matrix) if RXS=X(RXS=-X). The minimal and maximal ranks problems of matrix expression A-BXC with generalized reflective or skew-reflective matrices X are studied, and some solvability conditions of matrix equation BXC=A are derived.

Key words: generalized reflection matrices, generalized skew-reflective matrices, minimal and maximal ranks, matrix equations, generalized reflective matrices

中图分类号:

O241.6

代丽芳, 梁茂林, 何万生. 广义对称约束条件下矩阵表达式A-BXC 的极秩问题[J]. 山东大学学报（理学版）, 2015, 50(02): 90-94.

DAI Li-fang, LIANG Mao-lin, HE Wan-sheng. The minimal and maximal ranks problems of matrix expression A-BXC under generalized symmetric constraints[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 90-94.

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广义对称约束条件下矩阵表达式A-BXC 的极秩问题

The minimal and maximal ranks problems of matrix expression A-BXC under generalized symmetric constraints

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