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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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
Online AccessGet full text
ISSN0308-1087
1563-5139
DOI10.1080/03081080108818701

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Abstract 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.
AbstractList 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.
Author Tian, Yongge
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Cites_doi 10.1007/BF01385696
10.1016/S0024-3795(98)00008-1
10.1080/03081087408817070
10.1016/S0024-3795(99)00269-4
10.1016/0024-3795(92)90206-P
10.1016/0024-3795(85)90055-2
10.1007/BF02009557
10.1016/S0024-3795(98)10049-6
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Snippet 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...
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SubjectTerms AMS Subject Classifications:15A03, 15A09
Drazin inverse
Moore-Penrose inverse
Outer inverse
Rank
Weighted Moore-Penrose inverse
Title Rank equalities related to outer inverses of matrices and applications
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