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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/142375
Ver los metadatos del registro completo
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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:UNLP2025-09-29T11:32:27Zoai: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:13292025-09-29 11:32:28.027SEDICI (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 |
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http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) |
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application/pdf |
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