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...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/63775 |
| Online Access: | https://riunet.upv.es/handle/10251/63775 |
| Access Level: | Open access |
| Keyword: | Quadratic matrix Generalized quadratic matrix Idempotent matrix Spectrum Linear combination Diagonalization MATEMATICA APLICADA |
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On the spectra of some combinations of two generalized quadratic matricesPetik, TugbaOZDEMIR, HalimBenítez López, Julio|||0000-0002-3222-3036Quadratic matrixGeneralized quadratic matrixIdempotent matrixSpectrumLinear combinationDiagonalizationMATEMATICA APLICADA[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.ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarRepositorio Institucional de la Universitat Politècnica de València Riunet20152015-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/63775reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/637752026-06-13T07:49:27Z |
| dc.title.none.fl_str_mv |
On the spectra of some combinations of two generalized quadratic matrices |
| title |
On the spectra of some combinations of two generalized quadratic matrices |
| spellingShingle |
On the spectra of some combinations of two generalized quadratic matrices Petik, Tugba Quadratic matrix Generalized quadratic matrix Idempotent matrix Spectrum Linear combination Diagonalization MATEMATICA APLICADA |
| title_short |
On the spectra of some combinations of two generalized quadratic matrices |
| title_full |
On the spectra of some combinations of two generalized quadratic matrices |
| title_fullStr |
On the spectra of some combinations of two generalized quadratic matrices |
| title_full_unstemmed |
On the spectra of some combinations of two generalized quadratic matrices |
| title_sort |
On the spectra of some combinations of two generalized quadratic matrices |
| dc.creator.none.fl_str_mv |
Petik, Tugba OZDEMIR, Halim Benítez López, Julio|||0000-0002-3222-3036 |
| author |
Petik, Tugba |
| author_facet |
Petik, Tugba OZDEMIR, Halim Benítez López, Julio|||0000-0002-3222-3036 |
| author_role |
author |
| author2 |
OZDEMIR, Halim Benítez López, Julio|||0000-0002-3222-3036 |
| author2_role |
author author |
| dc.contributor.none.fl_str_mv |
Escuela Técnica Superior de Ingeniería de Telecomunicación Departamento de Matemática Aplicada Instituto Universitario de Matemática Multidisciplinar Repositorio Institucional de la Universitat Politècnica de València Riunet |
| dc.subject.none.fl_str_mv |
Quadratic matrix Generalized quadratic matrix Idempotent matrix Spectrum Linear combination Diagonalization MATEMATICA APLICADA |
| topic |
Quadratic matrix Generalized quadratic matrix Idempotent matrix Spectrum Linear combination Diagonalization MATEMATICA APLICADA |
| description |
[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. |
| publishDate |
2015 |
| dc.date.none.fl_str_mv |
2015 2015-10-01 |
| dc.type.none.fl_str_mv |
journal article http://purl.org/coar/resource_type/c_6501 VoR http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.none.fl_str_mv |
https://riunet.upv.es/handle/10251/63775 |
| url |
https://riunet.upv.es/handle/10251/63775 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Reserva de todos los derechos http://rightsstatements.org/vocab/InC/1.0/ |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Reserva de todos los derechos http://rightsstatements.org/vocab/InC/1.0/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Elsevier |
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Elsevier |
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reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname:Universitat Politècnica de València (UPV) |
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Universitat Politècnica de València (UPV) |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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