On the spectra of some combinations of two generalized quadratic matrices
[EN] Let A and B be two generalized quadratic matrices with respect to idempotent matrices P and Q, respectively, such that (A − αP)(A − βP) = 0, AP = PA = A, (B − γ Q)(B − δQ) = 0, BQ = QB = B, PQ = QP, AB = BA, and (A + B)(αβP − γδQ) = (αβP − γδQ)(A + B) with α,β, γ , δ ∈ C. Let A + B be diagonali...
| 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:10251/63775 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/63775 |
| Access Level: | acceso abierto |
| Palabra clave: | Quadratic matrix Generalized quadratic matrix Idempotent matrix Spectrum Linear combination Diagonalization MATEMATICA APLICADA |
| Sumario: | [EN] Let A and B be two generalized quadratic matrices with respect to idempotent matrices P and Q, respectively, such that (A − αP)(A − βP) = 0, AP = PA = A, (B − γ Q)(B − δQ) = 0, BQ = QB = B, PQ = QP, AB = BA, and (A + B)(αβP − γδQ) = (αβP − γδQ)(A + B) with α,β, γ , δ ∈ C. Let A + B be diagonalizable. The relations between the spectrum of the matrix A + B and the spectra of some matrices produced from A and B are considered. Moreover, some results on the spectrum of the matrix A + B are obtained when A + B is not diagonalizable. Finally, some results and examples illustrating the applications of the results in the work are given. © 2015 Elsevier Inc. All rights reserved. |
|---|