# Invariance under outer inverses

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 $${\mathbb {F}}$$ F , that the triplet $$B\hat{A}C$$ B A ^ C is invariant under all choices of outer inverses of A if and only if $$B = 0$$ B = 0 or $$C = 0$$ C = 0 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png aequationes mathematicae Springer Journals

# Invariance under outer inverses

, Volume 92 (2) – Dec 27, 2017
9 pages

/lp/springer_journal/invariance-under-outer-inverses-C5KZRTV7k8
Publisher
Springer Journals
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Combinatorics
ISSN
0001-9054
eISSN
1420-8903
D.O.I.
10.1007/s00010-017-0524-5
Publisher site
See Article on Publisher Site

### Abstract

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 $${\mathbb {F}}$$ F , that the triplet $$B\hat{A}C$$ B A ^ C is invariant under all choices of outer inverses of A if and only if $$B = 0$$ B = 0 or $$C = 0$$ C = 0 .

### Journal

aequationes mathematicaeSpringer Journals

Published: Dec 27, 2017

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