On common generalized inverses of a pair of matrices

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 and are also investigated. In addition,...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 54; no. 3; pp. 195 - 209
Main Authors Tian, Yongge, Takane, Yoshio
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2006
Subjects
AMS Subject Classifications: 15A03
Generalized inverses
Range equality
Rank formulas for partitioned matrices
Set equality
Set inclusion
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ISSN0308-1087
1563-5139
DOI10.1080/03081080500286560

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Summary: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 and are also investigated. In addition, some consequences and applications are given.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081080500286560