SEP矩阵的性质  

Researches of SEP matrices

作　　者：李金 王龙[1] 魏俊潮[1] LI Jin;WANG Long;WEI Junchao(School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2023年第2期1-5,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11901510);江苏省自然科学基金资助项目(BK20170589)。

摘　　要：为刻画群可逆条件下SEP矩阵的性质,通过替换SEP矩阵刻画式中某些矩阵为未知量的方法构造了新的方程,并利用新方程的可解性给出SEP矩阵的存在性准则.运用单变量矩阵方程和双变量矩阵方程在给定集合中的有解性方法,讨论了SEP矩阵的相关性质.结果表明:若A∈C^(n×n)是一个群可逆矩阵,则A是SEP矩阵当且仅当AXA^(#)=(A^(#))^(H)XA^(+),AXA^(#)AY=(A^(#))^(H)XY在ρ^(2)_(A)={(α,β)|α,β∈ρ_(A)}中可解,其中ρ_(A)={A,A^(#),A^(+),A^(H),(A^(#))^(H),(A^(+))^(H),(A^(+))^(#),(A^(#))^(+)}.This paper mainly studies the property of SEP matrix under the condition of the group invertibility. In terms of replacing the unknown elements in the characterizations of SEP matrix to construct the new matrix equation, the existence criteria are given by using the solvability of new equations. The properties of SEP matrix are studied by focusing on the solvability of a single variable matrix equations and bivariate matrix equations in a given set.The results show that if A∈C^(n×n) is a group invertible matrix,then it can be concluded that AXA^(#)=(A^(#))^(H) XA^(+),AXA^(#)AY=(A^(#))^(H) XY have at least one solution in the setρ^(2)_(A)={(α,β)|α,β∈ρ_(A)}if and only if A is SEP,where ρ_(A)={A,A^(#),A^(+),A^(H),(A^(#))^(H),(A^(+))^(H),(A^(+))^(#),(A^(#))^(+)}.

关 键 词：群可逆矩阵 Moore-Penrose逆矩阵 EP矩阵 SEP矩阵 

分 类 号：O151.21[理学—数学]