Eigenstructure of rank one updated matrices

[EN] The relationship among eigenvalues of a given square matrix A and the rank one updated matrix A+vkq⁎, where vk is an eigenvector of A associated with the eigenvalue λk and q is an arbitrary vector, was described by Brauer in 1952. In this work we study the relations between the Jordan structure...

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Detalles Bibliográficos
Autores: Bru García, Rafael, Cantó Colomina, Rafael|||0000-0002-1341-2800, Urbano Salvador, Ana María|||0000-0001-8590-1243
Tipo de recurso: artículo
Fecha de publicación:2015
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:10251/66417
Acceso en línea:https://riunet.upv.es/handle/10251/66417
Access Level:acceso abierto
Palabra clave:One rank perturbation
Jordan form
Jordan chains
MATEMATICA APLICADA
Descripción
Sumario:[EN] The relationship among eigenvalues of a given square matrix A and the rank one updated matrix A+vkq⁎, where vk is an eigenvector of A associated with the eigenvalue λk and q is an arbitrary vector, was described by Brauer in 1952. In this work we study the relations between the Jordan structures of A and A+vkq⁎. More precisely, we analyze the generalized eigenvectors of the updated matrix in terms of the generalized eigenvectors of A, as well as the Jordan chains of the updated matrix. Further, we obtain similar results when we use a generalized eigenvector of A instead of the eigenvector vk