On common generalized inverses of a pair of matrices

被引：5

作者：

Tian, YG ^{[1
]}

Takane, Y

机构：

[1] Shanghai Univ Finance & Econ, Sch Econ, Shanghai 200433, Peoples R China

[2] McGill Univ, Dept Psychol, Montreal, PQ H3A 1B1, Canada

来源：

LINEAR & MULTILINEAR ALGEBRA | 2006年 / 54卷 / 03期

关键词：

generalized inverses; rank formulas for partitioned matrices; range equality; set inclusion; set equality;

D O I：

10.1080/03081080500286560

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Necessary and sufficient conditions are established for a pair of matrices of the same size to have a common {1}-inverse, {1,2}-inverse, {1,3}-inverse, {1,4}-inverse, {1,2,3}-inverse and {1,2,4}-inverse, {1,3,4}-inverse, respectively. The relations between (A*)(-) and (A(-))* are also investigated. In addition, some consequences and applications are given.

引用

页码：195 / 209

页数：15

共 14 条

[1]

[Anonymous], 1971, GEN INVERSES MATRICE

[2]

Ben-Israel A., 2003, GEN INVERSES THEORY, V15

[3]

Campbell S.L., 1991, Generalized Inverses of Linear Transformations

[4]

Marsaglia G., 1974, LINEAR MULTILINEAR A, V2, P269, DOI DOI 10.1080/03081087408817070

[5] A PAIR OF SIMULTANEOUS LINEAR MATRIX EQUATIONS A1XB1=C1, A2XB2=C2 AND A MATRIX PROGRAMMING PROBLEM [J].

MITRA, SK .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 131 :107-123

[6] THE MINUS PARTIAL ORDER AND THE SHORTED MATRIX [J].

MITRA, SK .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1986, 83 :1-27

[7]

Tian Y., 2003, NEW YORK J MATH, V9, P345

[8]

Tian Y., 2002, MISSOURI J MATH SCI, V14, P40

[9]

Tian Y., 2002, SEA B MATH, V25, P745, DOI [10.1007/s100120200015, DOI 10.1007/S100120200015]

[10]

TIAN Y, UNPUB MAXIMAL RANKS

← 1 2 →