[1]陈永林.长方矩阵的加权群逆的存在条件与表示[J].南京师大学报(自然科学版),2008,31(03):1-5.
　Chen Yonglin.Existence Conditions and Expressions for Weighted Group Inverses of Rectangular Matrices[J].Journal of Nanjing Normal University(Natural Science Edition),2008,31(03):1-5.
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长方矩阵的加权群逆的存在条件与表示()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第31卷
期数:
2008年03期
页码:
1-5
栏目:
数学
出版日期:
2008-09-30

文章信息/Info

Title:
Existence Conditions and Expressions for Weighted Group Inverses of Rectangular Matrices
作者:
陈永林;
南京师范大学数学与计算机科学学院, 江苏南京210097
Author(s):
Chen Yonglin
School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China
关键词:
加权群逆;  定义方程;  存在条件;  表示
Keywords:
w eigh ted group inve rse;  de fining equation;  ex istence condition;  expression
分类号:
O151.21
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.
Abstract:
Cen has defined a w eighted group inverse o f rectangularm a trices. Let AI Cm @ n and WI Cn @m . If XI Cm @ n satisfies the sy stem of m atr ix equations (W 1)AWXWA = A, (W2)XWAWX = X, (W3)AWX = XWA, then X is called thew e ighted g roup inverse of A and denoted byA# W. New ex istence conditions and new expressions for the inverse A# W w ere g iven, and an ex istence cond ition and several express ions fo r the w eigh ted group inve rseAg, W o fA defined by C line and Grev ille w ere a lso g iven.

参考文献/References:

[ 1] 岑建苗. 关于长方矩阵的加权群逆的存在性[ J] . 计算数学, 2007, 29( 1): 39-48.
[ 2] C line R E, Grev ille T N E. A Drazin inverse fo r rec tangu larm atrices[ J]. Linear A lgebra App,l 1980, 29: 53-62.
[ 3] 陈永林. 广义逆矩阵的理论与方法[M ]. 南京: 南京师范大学出版社, 2005.
[ 4] Ben- Israe l A, G rev ille T N E. Gene ra lized Inverses: Theory and Applica tions[M ]. 2nd. N ew York: Springer, 2003.

备注/Memo

备注/Memo:
基金项目: 江苏省自然科学基金( BK2006725 )资助项目.
通讯联系人: 陈永林, 教授, 研究方向: 计算数学与广义逆矩阵论
更新日期/Last Update: 2013-05-05