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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Detalles Bibliográficos
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
Descripción
Sumario: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.