长方矩阵的加权群逆的存在条件与表示  

Existence Conditions and Expressions for Weighted Group Inverses of Rectangular Matrices

作　　者：陈永林[1] 

机构地区：[1]南京师范大学数学与计算机科学学院,江苏南京210097

出　　处：《南京师大学报（自然科学版）》2008年第3期1-5,共5页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：江苏省自然科学基金(BK2006725)资助项目

摘　　要：岑建苗定义了长方阵的加权群逆:设A∈Cm×n,W∈Cn×m.若X∈Cm×n适合矩阵方程组(W1)AWXWA=A,(W2)XWAWX=X,(W3)AWX=XWA,则称X为A的加W权群逆,记作AW#.本文给出了加权群逆AW#的许多新的存在条件与新的表示,并研究了Cline与Greville定义的加权群逆的存在条件与表示.Cen has defined a weighted group inverse of rectangular matrices. Let A∈C^m×n and W∈C^n×m,If X∈C^m×n satisfies the system of matrix equations （W1）AWXWA =A, （W2）XWAWX=X, （W3）AWX =XWA,then X is called the weighted group inverse of A and denoted by A^#W. New existence conditions and new expressions for the inverse A^#W given, and an AW were existence condition and several expressions for the weighted group inverse Ag,w of A defined by Cline and Greville were also given.

关 键 词：加权群逆 定义方程 存在条件 表示 

分 类 号：O241.6[理学—计算数学]