Representations and symbolic computation 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/10017/50516DOI: 10.1016/j.amc.2021.126287
ISSN: 0096-3003
Publisher
Elsevier
Date
2021-10-01Embargo end date
2023-10-01Funders
Agencia Estatal de investigación
Universidad de Alcalá
Bibliographic citation
Stanimirovic, P.S., Ciric, M. Lastra, A., Sendra, J.R. & Sendra, J. 2021, “Representations and symbolic computation of generalized inverses over fields”, Applied Mathematics and Computation, vol. 406, art. no. 126287.
Keywords
Outer inverse
Inner inverse
Matrix equation
Computer algebra
Specialization of matrices
Matrices with functional entries
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88796-P/ES/COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS 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/10.1016/j.amc.2021.126287Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2021 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
This paper investigates representations of outer matrix inverses with prescribed range and/or none space in terms of inner inverses. Further, required inner inverses are computed as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME. Using symbolic solutions to these matrix equations it is possible to derive corresponding algorithms in appropriate computer algebra systems. In addition, we give sufficient conditions to ensure the proper specialization of the presented representations. As a consequence, we derive algorithms to deal with outer inverses with prescribed range and/or none space and with meromorphic functional entries.
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