On the roots of coquaternions

Detalhes bibliográficos
Autor(a) principal: Falcão, M. I.
Data de Publicação: 2018
Outros Autores: Miranda, Fernando, Severino, Ricardo, Soares, M. J.
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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spelling 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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