Invariance under outer inverses

We shall use the minus partial order combined with Pierce’s decomposition to derive the class of outer inverses for idempotents, units and group invertible elements. Subsequently we show, for matrices over a field F , that the triplet B A ^ C is invariant under all choices of outer inverses of A if...

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Bibliographic Details
Published inAequationes mathematicae Vol. 92; no. 2; pp. 375 - 383
Main Authors Hartwig, R. E., Patrício, P.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2018
Subjects
Analysis
Combinatorics
Mathematics
Mathematics and Statistics
Outer inverses
Invariance
Regularity
15A09
16E50
Pierce decomposition
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Summary:We shall use the minus partial order combined with Pierce’s decomposition to derive the class of outer inverses for idempotents, units and group invertible elements. Subsequently we show, for matrices over a field F , that the triplet B A ^ C is invariant under all choices of outer inverses of A if and only if B = 0 or C = 0 .
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-017-0524-5