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Existence Conditions and Expressions for Weighted Group Inverses of Rectangular Matrices(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2008年03期
Page:
1-5
Research Field:
数学
Publishing date:

Info

Title:
Existence Conditions and Expressions for Weighted Group Inverses of Rectangular Matrices
Author(s):
Chen Yonglin
School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China
Keywords:
w eigh ted group inve rse;  de fining equation;  ex istence condition;  expression
PACS:
O151.21
DOI:
-
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.

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.

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Last Update: 2013-05-05