On the roots of coquaternions
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/59326 |
Resumo: | In this paper we give a complete characterization of the nth roots of a coquaternion q. In particular, we show that the number and type of roots-isolated and/or hyperboloidal-depend on the nature of q, on the parity of n and (eventually) on the sign of the real part of q. We also show how the coquaternionic formalism can be used to obtain, in a simple manner, explicit expressions for the real nth roots of any 2 x 2 real matrix. |
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On the roots of coquaternionsCoquaternionsRootsPolar formSimilarity class and quasi-similarity class of a coquaternionMatrix equationsCiências Naturais::MatemáticasScience & TechnologyIn this paper we give a complete characterization of the nth roots of a coquaternion q. In particular, we show that the number and type of roots-isolated and/or hyperboloidal-depend on the nature of q, on the parity of n and (eventually) on the sign of the real part of q. We also show how the coquaternionic formalism can be used to obtain, in a simple manner, explicit expressions for the real nth roots of any 2 x 2 real matrix.Research at CMAT was financed by Portuguese Funds through FCT - Fundacao para a Ciencia e a Tecnologia, within the Project UID/MAT/00013/2013. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC's (Fundacao para a Ciencia e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on "Competitiveness and Internationalization-COMPETE 2020" under the PT2020 Partnership Agreement.info:eu-repo/semantics/publishedVersionSpringerUniversidade do MinhoFalcão, M. I.Miranda, FernandoSeverino, RicardoSoares, M. J.2018-11-012018-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/59326eng0188-70091661-490910.1007/s00006-018-0914-3https://link.springer.com/article/10.1007%2Fs00006-018-0914-3info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:50:36Zoai:repositorium.sdum.uminho.pt:1822/59326Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:49:20.043580Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On the roots of coquaternions |
title |
On the roots of coquaternions |
spellingShingle |
On the roots of coquaternions Falcão, M. I. Coquaternions Roots Polar form Similarity class and quasi-similarity class of a coquaternion Matrix equations Ciências Naturais::Matemáticas Science & Technology |
title_short |
On the roots of coquaternions |
title_full |
On the roots of coquaternions |
title_fullStr |
On the roots of coquaternions |
title_full_unstemmed |
On the roots of coquaternions |
title_sort |
On the roots of coquaternions |
author |
Falcão, M. I. |
author_facet |
Falcão, M. I. Miranda, Fernando Severino, Ricardo Soares, M. J. |
author_role |
author |
author2 |
Miranda, Fernando Severino, Ricardo Soares, M. J. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Falcão, M. I. Miranda, Fernando Severino, Ricardo Soares, M. J. |
dc.subject.por.fl_str_mv |
Coquaternions Roots Polar form Similarity class and quasi-similarity class of a coquaternion Matrix equations Ciências Naturais::Matemáticas Science & Technology |
topic |
Coquaternions Roots Polar form Similarity class and quasi-similarity class of a coquaternion Matrix equations Ciências Naturais::Matemáticas Science & Technology |
description |
In this paper we give a complete characterization of the nth roots of a coquaternion q. In particular, we show that the number and type of roots-isolated and/or hyperboloidal-depend on the nature of q, on the parity of n and (eventually) on the sign of the real part of q. We also show how the coquaternionic formalism can be used to obtain, in a simple manner, explicit expressions for the real nth roots of any 2 x 2 real matrix. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-11-01 2018-11-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/59326 |
url |
http://hdl.handle.net/1822/59326 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0188-7009 1661-4909 10.1007/s00006-018-0914-3 https://link.springer.com/article/10.1007%2Fs00006-018-0914-3 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133073947754496 |