正规矩阵的方程构造  

Equation Construction of Normal Matrix

作　　者：方静雯 徐陈炜 曾立 魏俊潮[1] FANG Jingwen;XU Chenwei;ZENG Li;WEI Junchao(School of Mathematics Science,Yangzhou University,Yangzhou Jiangsu 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《大学数学》2022年第6期116-119,共4页College Mathematics

基　　金：国家自然科学基金(1941267721);2021年扬州大学大学生科创基金项目(X20210239);江苏高校品牌专业建设工程资助项目(数学与应用数学PPZY2015B109)。

摘　　要：通过对复数域上的群逆矩阵、Moore-Penrose(简称MP)可逆矩阵和共轭转置矩阵的研究,给出矩阵range-Hermitian(简称EP)性的一些新刻画,借助于这些性质刻画,构造出相关的矩阵方程,研究所得方程在给定集合中解的存在性对矩阵EP性的影响,从而给出正规矩阵的刻画.利用这些刻画再反过来构造矩阵方程,研究其一般解形式,通过变化其特解形式给出矩阵EP性的若干新性质.By studying the group invertible matrix,MP matrix and conjugate transpose matrix in complex field,this paper gives some new characterizations of ep-property of matrix,with the help of these characterizations,the related matrix equations are constructed,and the influence of the existence of the solution of the equation on ep-property of matrix in a given set is studied,and the characterization of EP-matrix is given.Using these characterizations,the matrix equation is constructed in turn,the general solution form is studied,and some new properties of EP property of matrix are given by changing the special solution form.

关 键 词：群可逆矩阵 EP矩阵 正规矩阵 矩阵方程的一般解 

分 类 号：O153[理学—数学]