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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/135380
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:51:11Zoai: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:34982025-09-29 09:51:11.969CONICET 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 |
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1844613575020118016 |
score |
13.070432 |