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On a formula of Thompson and McEnteggert for the adjugate matrix

dc.contributor.authorCastillo, Kenier
dc.contributor.authorZaballa Tejada, Juan Bernardo ORCID
dc.date.accessioned2022-02-14T08:52:25Z
dc.date.available2022-02-14T08:52:25Z
dc.date.issued2022
dc.identifier.citationLinear algebra and its applications 637 : 37-56 (2022)es_ES
dc.identifier.issn0024-3795
dc.identifier.issn1873-1856
dc.identifier.urihttp://hdl.handle.net/10810/55472
dc.description.abstractFor an eigenvalue lambda(0) of a Hermitian matrix A, the formula of Thompson and McEnteggert gives an explicit expression of the adjugate of lambda I-0 - A, Adj(lambda I-0 - A), in terms of eigenvectors of Afor lambda(0) and all its eigenvalues. In this paper Thompson-McEnteggert's formula is generalized to include any matrix with entries in an arbitrary field. In addition, for any nonsingular matrix A, a formula for the elementary divisors of Adj(A) is provided in terms of those of A. Finally, a generalization of the eigenvalue-eigenvector identity and three applications of the Thompson-McEnteggert's formula are presented.es_ES
dc.description.sponsorshipPartially supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES. Partially supported by "Ministerio de Economia, Industria y Competitividad (MINECO)" of Spain and "Fondo Europeo de Desarrollo Regional (FEDER)" of EU through grants MTM2017-83624-P and MTM2017-90682-REDT, and by UPV/EHU through grant GIU16/42.es_ES
dc.language.isoenges_ES
dc.publisherElsevieres_ES
dc.relationinfo:eu-repo/grantAgreement/MINECO/MTM2017-83624-Pes_ES
dc.relationinfo:eu-repo/grantAgreement/MINECO/MTM2017-90682-REDTes_ES
dc.rightsinfo:eu-repo/semantics/openAccesses_ES
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subjectadjugatees_ES
dc.subjecteigenvalueses_ES
dc.subjecteigenvectorses_ES
dc.subjectelementary divisorses_ES
dc.subjectrank-one matriceses_ES
dc.subjectperturbation-theoryes_ES
dc.titleOn a formula of Thompson and McEnteggert for the adjugate matrixes_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.holderThis article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.es_ES
dc.rights.holderAtribución-NoComercial-SinDerivadas 3.0 España*
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0024379521003864?via%3Dihubes_ES
dc.identifier.doi10.1016/j.laa.2021.10.021
dc.departamentoesMatemática Aplicada, Estadística e Investigación Operativaes_ES
dc.departamentoeuMatematika aplikatua eta estatistikaes_ES


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This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.
Except where otherwise noted, this item's license is described as This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.