Finite rank perturbations of linear relations and matrix pencils

Autores
Leben, Leslie; Martinez Peria, Francisco Dardo; Philipp, Friedrich; Trunk, Carsten; Winkler, Henrik
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least n. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+ 1 and that this bound is sharp. The reason for this behavior is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.
Fil: Leben, Leslie. Technische Universität Ilmenau; Alemania
Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: Philipp, Friedrich. Technische Universität Ilmenau; Alemania
Fil: Trunk, Carsten. Technische Universität Ilmenau; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Winkler, Henrik. Technische Universität Ilmenau; Alemania
Materia
FINITE RANK PERTURBATIONS
JORDAN CHAINS
LINEAR RELATIONS
SINGULAR MATRIX PENCILS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/135380
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Finite rank perturbations of linear relations and matrix pencilsLeben, LeslieMartinez Peria, Francisco DardoPhilipp, FriedrichTrunk, CarstenWinkler, HenrikFINITE RANK PERTURBATIONSJORDAN CHAINSLINEAR RELATIONSSINGULAR MATRIX PENCILShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least n. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+ 1 and that this bound is sharp. The reason for this behavior is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.Fil: Leben, Leslie. Technische Universität Ilmenau; AlemaniaFil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; ArgentinaFil: Philipp, Friedrich. Technische Universität Ilmenau; AlemaniaFil: Trunk, Carsten. Technische Universität Ilmenau; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Winkler, Henrik. Technische Universität Ilmenau; AlemaniaBirkhauser Verlag Ag2021-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/135380Leben, Leslie; Martinez Peria, Francisco Dardo; Philipp, Friedrich; Trunk, Carsten; Winkler, Henrik; Finite rank perturbations of linear relations and matrix pencils; Birkhauser Verlag Ag; Complex Analysis and Operator Theory; 15; 2; 2-2021; 1-371661-8254CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s11785-021-01082-xinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11785-021-01082-xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:20:30Zoai:ri.conicet.gov.ar:11336/135380instacron: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:34982025-10-22 11:20:31.174CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite rank perturbations of linear relations and matrix pencils
title Finite rank perturbations of linear relations and matrix pencils
spellingShingle Finite rank perturbations of linear relations and matrix pencils
Leben, Leslie
FINITE RANK PERTURBATIONS
JORDAN CHAINS
LINEAR RELATIONS
SINGULAR MATRIX PENCILS
title_short Finite rank perturbations of linear relations and matrix pencils
title_full Finite rank perturbations of linear relations and matrix pencils
title_fullStr Finite rank perturbations of linear relations and matrix pencils
title_full_unstemmed Finite rank perturbations of linear relations and matrix pencils
title_sort Finite rank perturbations of linear relations and matrix pencils
dc.creator.none.fl_str_mv Leben, Leslie
Martinez Peria, Francisco Dardo
Philipp, Friedrich
Trunk, Carsten
Winkler, Henrik
author Leben, Leslie
author_facet Leben, Leslie
Martinez Peria, Francisco Dardo
Philipp, Friedrich
Trunk, Carsten
Winkler, Henrik
author_role author
author2 Martinez Peria, Francisco Dardo
Philipp, Friedrich
Trunk, Carsten
Winkler, Henrik
author2_role author
author
author
author
dc.subject.none.fl_str_mv FINITE RANK PERTURBATIONS
JORDAN CHAINS
LINEAR RELATIONS
SINGULAR MATRIX PENCILS
topic FINITE RANK PERTURBATIONS
JORDAN CHAINS
LINEAR RELATIONS
SINGULAR MATRIX PENCILS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least n. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+ 1 and that this bound is sharp. The reason for this behavior is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.
Fil: Leben, Leslie. Technische Universität Ilmenau; Alemania
Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: Philipp, Friedrich. Technische Universität Ilmenau; Alemania
Fil: Trunk, Carsten. Technische Universität Ilmenau; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Winkler, Henrik. Technische Universität Ilmenau; Alemania
description We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least n. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+ 1 and that this bound is sharp. The reason for this behavior is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.
publishDate 2021
dc.date.none.fl_str_mv 2021-02
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/11336/135380
Leben, Leslie; Martinez Peria, Francisco Dardo; Philipp, Friedrich; Trunk, Carsten; Winkler, Henrik; Finite rank perturbations of linear relations and matrix pencils; Birkhauser Verlag Ag; Complex Analysis and Operator Theory; 15; 2; 2-2021; 1-37
1661-8254
CONICET Digital
CONICET
url http://hdl.handle.net/11336/135380
identifier_str_mv Leben, Leslie; Martinez Peria, Francisco Dardo; Philipp, Friedrich; Trunk, Carsten; Winkler, Henrik; Finite rank perturbations of linear relations and matrix pencils; Birkhauser Verlag Ag; Complex Analysis and Operator Theory; 15; 2; 2-2021; 1-37
1661-8254
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s11785-021-01082-x
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11785-021-01082-x
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
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
_version_ 1846781697214906368
score 12.982451

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