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...

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Detalles Bibliográficos
Autores: Mingueza, David, Montoro, M. Eulàlia, Roca Martinez, Alicia|||0000-0003-1926-1895
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
Descripción
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.