Finite Rank Perturbations of Linear Relations and Matrix Pencils

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...

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Detalles Bibliográficos
Autores principales:	Leben, Leslie, Martínez Pería, Francisco Dardo, Philipp, Friedrich, Trunk, Carsten, Winkler, Henrik
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2021
Materias:	Ciencias Exactas Matemática Finite rank perturbations Linear relations Singular matrix pencils Jordan chains
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/142375
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-142375
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Ciencias Exactas Matemática Finite rank perturbations Linear relations Singular matrix pencils Jordan chains
spellingShingle	Ciencias Exactas Matemática Finite rank perturbations Linear relations Singular matrix pencils Jordan chains Leben, Leslie Martínez Pería, Francisco Dardo Philipp, Friedrich Trunk, Carsten Winkler, Henrik Finite Rank Perturbations of Linear Relations and Matrix Pencils
topic_facet	Ciencias Exactas Matemática Finite rank perturbations Linear relations Singular matrix pencils Jordan chains
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.
format	Articulo Articulo
author	Leben, Leslie Martínez Pería, Francisco Dardo Philipp, Friedrich Trunk, Carsten Winkler, Henrik
author_facet	Leben, Leslie Martínez Pería, Francisco Dardo Philipp, Friedrich Trunk, Carsten Winkler, Henrik
author_sort	Leben, Leslie
title	Finite Rank Perturbations of Linear Relations and 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
publishDate	2021
url	http://sedici.unlp.edu.ar/handle/10915/142375
work_keys_str_mv	AT lebenleslie finiterankperturbationsoflinearrelationsandmatrixpencils AT martinezperiafranciscodardo finiterankperturbationsoflinearrelationsandmatrixpencils AT philippfriedrich finiterankperturbationsoflinearrelationsandmatrixpencils AT trunkcarsten finiterankperturbationsoflinearrelationsandmatrixpencils AT winklerhenrik finiterankperturbationsoflinearrelationsandmatrixpencils
bdutipo_str	Repositorios
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Finite Rank Perturbations of Linear Relations and Matrix Pencils

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