Finite Rank Perturbations of Linear Relations and Matrix Pencils

Autores
Leben, Leslie; Martínez Pería, 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.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Matemática
Finite rank perturbations
Linear relations
Singular matrix pencils
Jordan chains
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/142375
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/142375
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Finite Rank Perturbations of Linear Relations and Matrix PencilsLeben, LeslieMartínez Pería, Francisco DardoPhilipp, FriedrichTrunk, CarstenWinkler, HenrikCiencias ExactasMatemáticaFinite rank perturbationsLinear relationsSingular matrix pencilsJordan chainsWe 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.Facultad de Ciencias Exactas2021-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/142375enginfo:eu-repo/semantics/altIdentifier/issn/1661-8254info:eu-repo/semantics/altIdentifier/issn/1661-8262info:eu-repo/semantics/altIdentifier/doi/10.1007/s11785-021-01082-xinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T17:13:22Zoai:sedici.unlp.edu.ar:10915/142375Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:13:22.355SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Ciencias Exactas
Matemática
Finite rank perturbations
Linear relations
Singular matrix pencils
Jordan chains
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
Martínez Pería, Francisco Dardo
Philipp, Friedrich
Trunk, Carsten
Winkler, Henrik
author Leben, Leslie
author_facet Leben, Leslie
Martínez Pería, Francisco Dardo
Philipp, Friedrich
Trunk, Carsten
Winkler, Henrik
author_role author
author2 Martínez Pería, Francisco Dardo
Philipp, Friedrich
Trunk, Carsten
Winkler, Henrik
author2_role author
author
author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
Finite rank perturbations
Linear relations
Singular matrix pencils
Jordan chains
topic Ciencias Exactas
Matemática
Finite rank perturbations
Linear relations
Singular matrix pencils
Jordan chains
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.
Facultad de Ciencias Exactas
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 2021-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/142375
url http://sedici.unlp.edu.ar/handle/10915/142375
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1661-8254
info:eu-repo/semantics/altIdentifier/issn/1661-8262
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11785-021-01082-x
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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