Rank equalities related to outer inverses of matrices and applications

A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin invers...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 49; no. 4; pp. 269 - 288
Main Author Tian, Yongge
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 15.12.2001
Subjects
AMS Subject Classifications:15A03, 15A09
Drazin inverse
Moore-Penrose inverse
Outer inverse
Rank
Weighted Moore-Penrose inverse
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Summary:A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin inverses and weighted Moore-Penrose inverses of matrices.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081080108818701