The centralizer of an endomorphism over an arbitrary field
[EN] The centralizer of an endomorphism of a finite dimensional vector space is known when the endomorphism is nonderogatory or when its minimal polynomial splits over the field. It is also known for the real Jordan canonical form. In this paper we characterize the centralizer of an endomorphism ove...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/161058 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/161058 |
| Access Level: | acceso abierto |
| Palabra clave: | Centralizer Companion matrices Nonseparable polynomials Generalized Jordan canonical form Generalized Weyr canonical form MATEMATICA APLICADA |
| Sumario: | [EN] The centralizer of an endomorphism of a finite dimensional vector space is known when the endomorphism is nonderogatory or when its minimal polynomial splits over the field. It is also known for the real Jordan canonical form. In this paper we characterize the centralizer of an endomorphism over an arbitrary field, and compute its dimension. The result is obtained via generalized Jordan canonical forms (for separable and nonseparable minimal polynomials). In addition, we also obtain the corresponding generalized Weyr canonical forms and the structure of its centralizers, which in turn allows us to compute the determinant of its elements. (C) 2020 Elsevier Inc. All rights reserved. |
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