Representations and geometrical properties of generalized inverses over fields
Authors
Stanimirovic, Predrag S.; Ciric, Miroslav; Lastra Sedano, Alberto; Sendra Pons, Juan Rafael; Sendra Pons, JuanaIdentifiers
Permanent link (URI): http://hdl.handle.net/10017/50372DOI: 10.1080/03081087.2021.1985420
ISSN: 0308-1087
Publisher
Taylor & Francis
Date
2021-10-07Embargo end date
2022-10-07Funders
Agencia Estatal de Investigación
Universidad de Alcalá
Bibliographic citation
Stanimirovic, P.S., Ciric, M., Lastra, A., Sendra, J.R. & Sendra, J. 2021, “Representations and geometrical properties of generalized inverses over fields”, Linear and Multilinear Algebra, DOI: 10.1080/03081087.2021.1985420.
Keywords
Outer inverses
Inner inverses
Moore-Penrose inverse
(B, C) inverse
Affine subspaces
Urquhart's formula
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113192GB-I00/ES/VISUALIZACION MATEMATICA: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105621GB-I00/ES/METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOS/
info:eu-repo/grantAgreement/UAH//CM-JIN-2019-010
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1080/03081087.2021.1985420Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2021 Taylor & Francis
Access rights
info:eu-repo/semantics/openAccess
Abstract
In this paper, as a generalization of Urquhart’s formulas, we present a full description of the sets
of inner inverses and (B, C)-inverses over an arbitrary field. In addition, identifying the matrix vector
space with an affine space, we analyze geometrical properties of the main generalized inverse sets. We
prove that the set of inner inverses, and the set of (B, C)-inverses, form affine subspaces and we study
their dimensions. Furthermore, under some hypotheses, we prove that the set of outer inverses is not
an affine subspace but it is an affine algebraic variety. We also provide lower and upper bounds for the
dimension of the outer inverse set.
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