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...
| Autores: | , , |
|---|---|
| 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 |
| 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 |
|---|