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Linear and Multilinear Algebra Volume 71, 2023 - Issue 18
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Research Article

On the explicit computation of the set of 1-inverses of a square matrix

Fernando Pablos RomoDepartamento de Matemáticas, Universidad de Salamanca, Salamanca, EspañaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0003-3444-1800View further author information
ORCID Icon &
Diego Alba AlonsoDepartamento de Matemáticas, Universidad de Salamanca, Salamanca, EspañaORCID Iconhttps://orcid.org/0000-0001-7147-8368View further author information
ORCID Icon
Pages 2869-2876 | Received 18 Jan 2022, Accepted 03 Sep 2022, Published online: 13 Sep 2022
 
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Abstract

The aim of this note is to offer a method for the explicit computation of all 1-inverses of an arbitrary square matrix. The main tool to obtain this algorithm is the characterization of the set of 1-inverses of a finite potent endomorphism.

2020 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first-named author of this work is partially supported by the Spanish Government research projects no. PGC2018-099599-B-I00 and the Regional Government of Castile and Leon research project no. J416/463AC03.

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