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...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/888 |
| Acesso em linha: | https://hdl.handle.net/2117/888 |
| Access Level: | acceso abierto |
| Palavra-chave: | 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 |
| Resumo: | 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. |
|---|