Perturbed marked reduced forms of invariant subspaces
The classification of invariant subspaces is an open problem related to other important ones like the Carlson problem. Here we obtain a reduced form of these invariant subspaces as a new tool to tackle these problems. In particular, it allows us to prove quite easily partial results already known. T...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:2117/134342 |
| Acceso en línea: | https://hdl.handle.net/2117/134342 https://dx.doi.org/10.1016/j.laa.2018.09.009 |
| Access Level: | acceso abierto |
| Palabra clave: | Vector spaces Endomorphisms (Group theory) Endomorphism invariant subspaces marked subspaces Espais vectorials Endomorfismes (Teoria de grups) Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::93 Systems Theory Control::93B Controllability, observability, and system structure Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | The classification of invariant subspaces is an open problem related to other important ones like the Carlson problem. Here we obtain a reduced form of these invariant subspaces as a new tool to tackle these problems. In particular, it allows us to prove quite easily partial results already known. The key point is assigning to each invariant subspace a marked one (its marked type) in order to partition the set of invariant subspaces in a finite number of subsets (the marked classes), each one containing only one marked subspace. Next, we parametrize (minimally) each marked class by means of the so-called PM reduced families, so that representatives of an invariant subspace (its PM reduced forms) appear in just one of these families. |
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