On the Lyapunov and Stein Equations, II

Detalhes bibliográficos
Autor(a) principal: Silva, F.C.
Data de Publicação: 2007
Outros Autores: Simões, R.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/8432
Resumo: Let L ∈ Cn × n and let H, K ∈ Cn × n be Hermitian matrices. Some already known results, including the general inertia theorem, give partial answers to the following problem: find a complete set of relations between the similarity class of L and the congruence classes of H and K, when the Lyapunov equation LH + HL* = K is satisfied. In this paper, we solve this problem when L is nonderogatory, H is nonsingular and K has at least one eigenvalue with positive real part and one eigenvalue with negative real part. Our result generalizes a previous paper by L. M. DeAlba. The corresponding problem with the Stein equation follows easily using a Cayley transform. © 2007 Elsevier Inc. All rights reserved.
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spelling On the Lyapunov and Stein Equations, IIInertia of matricesLyapunov equationStein equationLet L ∈ Cn × n and let H, K ∈ Cn × n be Hermitian matrices. Some already known results, including the general inertia theorem, give partial answers to the following problem: find a complete set of relations between the similarity class of L and the congruence classes of H and K, when the Lyapunov equation LH + HL* = K is satisfied. In this paper, we solve this problem when L is nonderogatory, H is nonsingular and K has at least one eigenvalue with positive real part and one eigenvalue with negative real part. Our result generalizes a previous paper by L. M. DeAlba. The corresponding problem with the Stein equation follows easily using a Cayley transform. © 2007 Elsevier Inc. All rights reserved.Elsevier2012-05-02T15:43:43Z2007-01-01T00:00:00Z2007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/8432eng0024-379510.1016/j.laa.2007.05.001Silva, F.C.Simões, R.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:07:01Zoai:ria.ua.pt:10773/8432Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:43:06.081865Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the Lyapunov and Stein Equations, II
title On the Lyapunov and Stein Equations, II
spellingShingle On the Lyapunov and Stein Equations, II
Silva, F.C.
Inertia of matrices
Lyapunov equation
Stein equation
title_short On the Lyapunov and Stein Equations, II
title_full On the Lyapunov and Stein Equations, II
title_fullStr On the Lyapunov and Stein Equations, II
title_full_unstemmed On the Lyapunov and Stein Equations, II
title_sort On the Lyapunov and Stein Equations, II
author Silva, F.C.
author_facet Silva, F.C.
Simões, R.
author_role author
author2 Simões, R.
author2_role author
dc.contributor.author.fl_str_mv Silva, F.C.
Simões, R.
dc.subject.por.fl_str_mv Inertia of matrices
Lyapunov equation
Stein equation
topic Inertia of matrices
Lyapunov equation
Stein equation
description Let L ∈ Cn × n and let H, K ∈ Cn × n be Hermitian matrices. Some already known results, including the general inertia theorem, give partial answers to the following problem: find a complete set of relations between the similarity class of L and the congruence classes of H and K, when the Lyapunov equation LH + HL* = K is satisfied. In this paper, we solve this problem when L is nonderogatory, H is nonsingular and K has at least one eigenvalue with positive real part and one eigenvalue with negative real part. Our result generalizes a previous paper by L. M. DeAlba. The corresponding problem with the Stein equation follows easily using a Cayley transform. © 2007 Elsevier Inc. All rights reserved.
publishDate 2007
dc.date.none.fl_str_mv 2007-01-01T00:00:00Z
2007
2012-05-02T15:43:43Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/8432
url http://hdl.handle.net/10773/8432
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0024-3795
10.1016/j.laa.2007.05.001
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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