THE MOORE IDEMPOTENTS OF A MATRIX

被引：3
作者：
ROBINSON, DW
机构：
[1] Department of Mathematics Brigham Young University Provo
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 1994年 / 211卷
关键词：
D O I：
10.1016/0024-3795(94)90079-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let R be a commutative ring with 1 and with an involution-, and let M(R) be the category of finite matrices over R with the involution (a(ij)) --> (a(ji))* = (aBAR(ji)). If A is in M(R), then there exists a unique list (e0,...,e(s)) of pairwise orthogonal symmetric idempotents of R that are characterized by several properties involving the rank and squared volume of the e(i) A. In particular, A has a Moore-Penrose inverse in M(R) iff e(s) A = 0.
引用
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页码：15 / 26
页数：12
相关论文
共 7 条
[1]   THE MOORE-PENROSE INVERSE OVER A COMMUTATIVE RING [J].
BAPAT, RB ;
ROBINSON, DW .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 177 :89-103
[2]  
BAPAT RB, 1990, LINEAR ALGEBRA APPL, V140, P180
[3]   A VOLUME ASSOCIATED WITH MXN MATRICES [J].
BENISRAEL, A .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 167 :87-111
[4]  
Moore EH, 1920, B AM MATH SOC, V2, P394, DOI [DOI 10.1090/S0002-9904-1920-03322-7, 10.1090/S0002-9904-1920-03322-7]
[5]   SYMMETRIC MORPHISMS AND THE EXISTENCE OF MOORE-PENROSE INVERSES [J].
PUYSTJENS, R ;
ROBINSON, DW .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 131 :51-69
[6]  
PUYSTJENS R, GROUP PENROSE INVERS
[7]   CATEGORIES OF MATRICES WITH ONLY OBVIOUS MOORE-PENROSE INVERSES [J].
ROBINSON, DW ;
PUYSTJENS, R ;
VANGEEL, J .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 97 :93-102
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