On a class of non-Hermitian matrices with positive definite Schur complements
- Autores
- Berger, Thomas; Giribet, Juan Ignacio; Martinez Peria, Francisco Dardo; Trunk, Carsten Joachim
- Año de publicación
- 2019
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite Schur complement with respect to its submatrix A. Additionally, we show that K can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces.
Fil: Berger, Thomas. Universitat Hamburg; Alemania
Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; Argentina
Fil: Martinez Peria, Francisco Dardo. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Trunk, Carsten Joachim. Technische Universitat Ilmenau. Institut Fur Mathematik; Alemania - Materia
-
FRAMES
KREIN SPACES
COMPLEMENTO DE SCHUR
OPERATOR DE CORTO-CIRCUITO - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/107578
Ver los metadatos del registro completo
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On a class of non-Hermitian matrices with positive definite Schur complementsBerger, ThomasGiribet, Juan IgnacioMartinez Peria, Francisco DardoTrunk, Carsten JoachimFRAMESKREIN SPACESCOMPLEMENTO DE SCHUROPERATOR DE CORTO-CIRCUITOhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite Schur complement with respect to its submatrix A. Additionally, we show that K can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces.Fil: Berger, Thomas. Universitat Hamburg; AlemaniaFil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; ArgentinaFil: Martinez Peria, Francisco Dardo. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Trunk, Carsten Joachim. Technische Universitat Ilmenau. Institut Fur Mathematik; AlemaniaAmerican Mathematical Society2019-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/107578Berger, Thomas; Giribet, Juan Ignacio; Martinez Peria, Francisco Dardo; Trunk, Carsten Joachim; On a class of non-Hermitian matrices with positive definite Schur complements; American Mathematical Society; Proceedings of the American Mathematical Society; 147; 6; 3-2019; 2375-23880002-99391088-6826CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2019-147-06/S0002-9939-2019-14412-9/info:eu-repo/semantics/altIdentifier/doi/ 10.1090/proc/14412info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1807.08591info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:03:58Zoai:ri.conicet.gov.ar:11336/107578instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:03:58.688CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
On a class of non-Hermitian matrices with positive definite Schur complements |
title |
On a class of non-Hermitian matrices with positive definite Schur complements |
spellingShingle |
On a class of non-Hermitian matrices with positive definite Schur complements Berger, Thomas FRAMES KREIN SPACES COMPLEMENTO DE SCHUR OPERATOR DE CORTO-CIRCUITO |
title_short |
On a class of non-Hermitian matrices with positive definite Schur complements |
title_full |
On a class of non-Hermitian matrices with positive definite Schur complements |
title_fullStr |
On a class of non-Hermitian matrices with positive definite Schur complements |
title_full_unstemmed |
On a class of non-Hermitian matrices with positive definite Schur complements |
title_sort |
On a class of non-Hermitian matrices with positive definite Schur complements |
dc.creator.none.fl_str_mv |
Berger, Thomas Giribet, Juan Ignacio Martinez Peria, Francisco Dardo Trunk, Carsten Joachim |
author |
Berger, Thomas |
author_facet |
Berger, Thomas Giribet, Juan Ignacio Martinez Peria, Francisco Dardo Trunk, Carsten Joachim |
author_role |
author |
author2 |
Giribet, Juan Ignacio Martinez Peria, Francisco Dardo Trunk, Carsten Joachim |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
FRAMES KREIN SPACES COMPLEMENTO DE SCHUR OPERATOR DE CORTO-CIRCUITO |
topic |
FRAMES KREIN SPACES COMPLEMENTO DE SCHUR OPERATOR DE CORTO-CIRCUITO |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite Schur complement with respect to its submatrix A. Additionally, we show that K can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces. Fil: Berger, Thomas. Universitat Hamburg; Alemania Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; Argentina Fil: Martinez Peria, Francisco Dardo. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Trunk, Carsten Joachim. Technische Universitat Ilmenau. Institut Fur Mathematik; Alemania |
description |
Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite Schur complement with respect to its submatrix A. Additionally, we show that K can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-03 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/107578 Berger, Thomas; Giribet, Juan Ignacio; Martinez Peria, Francisco Dardo; Trunk, Carsten Joachim; On a class of non-Hermitian matrices with positive definite Schur complements; American Mathematical Society; Proceedings of the American Mathematical Society; 147; 6; 3-2019; 2375-2388 0002-9939 1088-6826 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/107578 |
identifier_str_mv |
Berger, Thomas; Giribet, Juan Ignacio; Martinez Peria, Francisco Dardo; Trunk, Carsten Joachim; On a class of non-Hermitian matrices with positive definite Schur complements; American Mathematical Society; Proceedings of the American Mathematical Society; 147; 6; 3-2019; 2375-2388 0002-9939 1088-6826 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2019-147-06/S0002-9939-2019-14412-9/ info:eu-repo/semantics/altIdentifier/doi/ 10.1090/proc/14412 info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1807.08591 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
American Mathematical Society |
publisher.none.fl_str_mv |
American Mathematical Society |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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