Characterizations of {K,s+1}-Potent Matrices and Applications
Recently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class of matrices that involve an involutory matrix, generalizing the well-known idemp...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2012 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositório: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglês |
| OAI Identifier: | oai:riunet.upv.es:10251/37709 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/37709 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Group inverse matrix Idempotent matrix Involutory matrix Spectrum Block representation Generalized inverse Group inverse Linear combinations Matrix Inverse problems Matrix algebra INGENIERIA TELEMATICA MATEMATICA APLICADA |
| Resumo: | Recently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class of matrices that involve an involutory matrix, generalizing the well-known idempotent matrix, widely useful in many applications. In this paper, we introduce a new kind of matrices called {K,s+1}-potent, as an extension of the aforementioned ones. First, different properties of {K,s+1}-potent matrices have been developed. Later, the main result developed in this paper is the characterization of this kind of matrices from a spectral point of view, in terms of powers of the matrix, by means of the group inverse and, via a block representation of a matrix of index 1. Finally, an application of the above results to study linear combinations of {K,s+1}-potent matrices is derived. © 2010 Elsevier Inc. All rights reserved. |
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