Dimension of the orbit of marked subspaces

Given a nilpotent endomorphism, we consider the manifold of invariant subspaces having a fixed Segre characteristic. In [Linear Algebra Appl., 332–334 (2001) 569], the implicit form of a miniversal deformation of an invariant subspace with respect to the usual equivalence relation between subspaces...

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Autores: Compta Creus, Albert|||0000-0003-2388-3283, Ferrer Llop, Josep|||0000-0003-3380-231X, Peña Carrera, Marta|||0000-0003-3889-8584
Tipo de recurso: artículo
Fecha de publicación:2004
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/888
Acceso en línea:https://hdl.handle.net/2117/888
Access Level:acceso abierto
Palabra clave:Global analysis (Mathematics)
Algebras, Linear
Multilinear algebra
Matrices
orbit of marked subspaces
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
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spelling Dimension of the orbit of marked subspacesCompta Creus, Albert|||0000-0003-2388-3283Ferrer Llop, Josep|||0000-0003-3380-231XPeña Carrera, Marta|||0000-0003-3889-8584Global analysis (Mathematics)Algebras, LinearMultilinear algebraMatricesorbit of marked subspacesÀlgebra linealÀlgebra multilinealMatriu S, TeoriaClassificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theoryClassificació AMS::15 Linear and multilinear algebramatrix theoryGiven a nilpotent endomorphism, we consider the manifold of invariant subspaces having a fixed Segre characteristic. In [Linear Algebra Appl., 332–334 (2001) 569], the implicit form of a miniversal deformation of an invariant subspace with respect to the usual equivalence relation between subspaces is obtained. Here we obtain the explicit form of this deformation when the invariant subspace is marked, and we use it to calculate the dimension of the orbit and in particular to characterize the stable marked subspaces (those with open orbit).Moreover, we study the rank of the endomorphisms in the quotient space by the subspaces in the miniversal deformation of the giving subspace.Peer Reviewed20042004-01-0120072007-05-04journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/888reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/8882026-05-27T15:37:01Z
dc.title.none.fl_str_mv Dimension of the orbit of marked subspaces
title Dimension of the orbit of marked subspaces
spellingShingle Dimension of the orbit of marked subspaces
Compta Creus, Albert|||0000-0003-2388-3283
Global analysis (Mathematics)
Algebras, Linear
Multilinear algebra
Matrices
orbit of marked subspaces
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
title_short Dimension of the orbit of marked subspaces
title_full Dimension of the orbit of marked subspaces
title_fullStr Dimension of the orbit of marked subspaces
title_full_unstemmed Dimension of the orbit of marked subspaces
title_sort Dimension of the orbit of marked subspaces
dc.creator.none.fl_str_mv Compta Creus, Albert|||0000-0003-2388-3283
Ferrer Llop, Josep|||0000-0003-3380-231X
Peña Carrera, Marta|||0000-0003-3889-8584
author Compta Creus, Albert|||0000-0003-2388-3283
author_facet Compta Creus, Albert|||0000-0003-2388-3283
Ferrer Llop, Josep|||0000-0003-3380-231X
Peña Carrera, Marta|||0000-0003-3889-8584
author_role author
author2 Ferrer Llop, Josep|||0000-0003-3380-231X
Peña Carrera, Marta|||0000-0003-3889-8584
author2_role author
author
dc.subject.none.fl_str_mv Global analysis (Mathematics)
Algebras, Linear
Multilinear algebra
Matrices
orbit of marked subspaces
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
topic Global analysis (Mathematics)
Algebras, Linear
Multilinear algebra
Matrices
orbit of marked subspaces
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory
Classificació AMS::15 Linear and multilinear algebra
matrix theory
description Given a nilpotent endomorphism, we consider the manifold of invariant subspaces having a fixed Segre characteristic. In [Linear Algebra Appl., 332–334 (2001) 569], the implicit form of a miniversal deformation of an invariant subspace with respect to the usual equivalence relation between subspaces is obtained. Here we obtain the explicit form of this deformation when the invariant subspace is marked, and we use it to calculate the dimension of the orbit and in particular to characterize the stable marked subspaces (those with open orbit).Moreover, we study the rank of the endomorphisms in the quotient space by the subspaces in the miniversal deformation of the giving subspace.
publishDate 2004
dc.date.none.fl_str_mv 2004
2004-01-01
2007
2007-05-04
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/888
url https://hdl.handle.net/2117/888
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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