Representations and geometrical properties of generalized inverses over fields
Autores
Stanimirovic, Predrag S.; Ciric, Miroslav; Lastra Sedano, Alberto; Sendra Pons, Juan Rafael; Sendra Pons, JuanaIdentificadores
Enlace permanente (URI): http://hdl.handle.net/10017/50372DOI: 10.1080/03081087.2021.1985420
ISSN: 0308-1087
Editor
Taylor & Francis
Fecha de publicación
2021-10-07Fecha fin de embargo
2022-10-07Patrocinadores
Agencia Estatal de Investigación
Universidad de Alcalá
Cita bibliográfica
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.
Palabras clave
Outer inverses
Inner inverses
Moore-Penrose inverse
(B, C) inverse
Affine subspaces
Urquhart's formula
Proyectos
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
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/acceptedVersion
Versión del editor
https://doi.org/10.1080/03081087.2021.1985420Derechos
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2021 Taylor & Francis
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
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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- MATEMATIC - Artículos [172]