On a class of non-Hermitian matrices with positive definite Schur complements

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 sh...

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Authors: Berger, Thomas, Giribet, Juan Ignacio, Martinez Peria, Francisco Dardo, Trunk, Carsten Joachim
Format: article
Status:Published version
Publication Date:2019
Country:Argentina
Institution:Consejo Nacional de Investigaciones Científicas y Técnicas
Repository:CONICET Digital (CONICET)
Language:English
OAI Identifier:oai:ri.conicet.gov.ar:11336/107578
Online Access:http://hdl.handle.net/11336/107578
Access Level:Open access
Keyword:FRAMES
KREIN SPACES
COMPLEMENTO DE SCHUR
OPERATOR DE CORTO-CIRCUITO
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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oai_identifier_str oai:ri.conicet.gov.ar:11336/107578
network_acronym_str AR
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repository_id_str
spelling 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 Técnicas2024-05-08T13:58:56Zoai: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:34982024-05-08 13:58:56.738CONICET 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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic FRAMES
KREIN SPACES
COMPLEMENTO DE SCHUR
OPERATOR DE CORTO-CIRCUITO
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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
_version_ 1799195640972967936
score 15.811543

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