Publicação
On the convexity and circularity of the numerical range of nilpotent quaternionic matrices
| Resumo: | We provide a sufficient condition for the numerical range of a nilpotent matrix N to be circular in terms of the existence of cycles in an undirected graph associated with N. We prove that if we add to this matrix N a diagonal real matrix D, the matrix D+N has convex numerical range. For 3 x 3 nilpotent matrices, we strength further our results and obtain necessary and sufficient conditions for circularity and convexity of the numerical range. |
|---|---|
| Autores principais: | Carvalho, L. |
| Outros Autores: | Mendes, S.; Diogo, C. |
| Assunto: | Quaternions Numerical range Nilpotent matrix |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | ISCTE |
| Idioma: | inglês |
| Origem: | Repositório ISCTE |
| _version_ | 1867301217536835584 |
|---|---|
| author | Carvalho, L. |
| author2 | Mendes, S. Diogo, C. |
| author2_role | author author |
| author_facet | Carvalho, L. Mendes, S. Diogo, C. |
| author_role | author |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Carvalho, L.\"},{\"Person.name\":\"Mendes, S.\"},{\"Person.name\":\"Diogo, C.\"}] |
| datacite.creators.creator.creatorName.fl_str_mv | Carvalho, L. Mendes, S. Diogo, C. |
| datacite.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2020-03-24T08:32:44Z |
| datacite.date.embargoed.fl_str_mv | 2020-03-24T08:32:44Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Quaternions Numerical range Nilpotent matrix |
| datacite.titles.title.fl_str_mv | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| dc.creator.none.fl_str_mv | Carvalho, L. Mendes, S. Diogo, C. |
| dc.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2020-03-24T08:32:44Z |
| dc.date.embargoed.fl_str_mv | 2020-03-24T08:32:44Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10071/20172 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Electronic Journals Project |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Quaternions Numerical range Nilpotent matrix |
| dc.title.fl_str_mv | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | We provide a sufficient condition for the numerical range of a nilpotent matrix N to be circular in terms of the existence of cycles in an undirected graph associated with N. We prove that if we add to this matrix N a diagonal real matrix D, the matrix D+N has convex numerical range. For 3 x 3 nilpotent matrices, we strength further our results and obtain necessary and sufficient conditions for circularity and convexity of the numerical range. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | iscte_8a632bae7e9ca6a2dfd3f94f58e38921 |
| identifier.url.fl_str_mv | http://hdl.handle.net/10071/20172 |
| instacron_str | iscte |
| institution | ISCTE |
| instname_str | ISCTE |
| language | eng |
| network_acronym_str | iscte |
| network_name_str | Repositório ISCTE |
| oai_identifier_str | oai:repositorio.iscte-iul.pt:10071/20172 |
| organization_str_mv | urn:organizationAcronym:iscte |
| person_str_mv | Carvalho, L. Mendes, S. Diogo, C. |
| publishDate | 2019 |
| publisher.none.fl_str_mv | Electronic Journals Project |
| reponame_str | Repositório ISCTE |
| repository_id_str | urn:repositoryAcronym:iscte |
| service_str_mv | urn:repositoryAcronym:iscte |
| spelling | engWe provide a sufficient condition for the numerical range of a nilpotent matrix N to be circular in terms of the existence of cycles in an undirected graph associated with N. We prove that if we add to this matrix N a diagonal real matrix D, the matrix D+N has convex numerical range. For 3 x 3 nilpotent matrices, we strength further our results and obtain necessary and sufficient conditions for circularity and convexity of the numerical range.application/pdfengElectronic Journals ProjectengOn the convexity and circularity of the numerical range of nilpotent quaternionic matricesCarvalho, L.Mendes, S.Diogo, C.Handlehttp://hdl.handle.net/10071/20172ISSNIsPartOf1076-98032020-03-24T08:32:44Z2019-01-01T00:00:00Z20192020-03-24T08:28:52Zhttp://purl.org/coar/access_right/c_abf2open accessengQuaternionsengNumerical rangeengNilpotent matrix397820 byteshttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.iscte-iul.pt/bitstreams/8804f5b9-d97d-4df5-b670-80fc49b53fb1/downloadliteraturehttp://purl.org/coar/resource_type/c_6501journal article |
| spellingShingle | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices Carvalho, L. Quaternions Numerical range Nilpotent matrix |
| status | SINGLETON |
| subject.fl_str_mv | Quaternions Numerical range Nilpotent matrix |
| title | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| title_full | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| title_fullStr | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| title_full_unstemmed | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| title_short | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| title_sort | On the convexity and circularity of the numerical range of nilpotent quaternionic matrices |
| topic | Quaternions Numerical range Nilpotent matrix |
| topic_facet | Quaternions Numerical range Nilpotent matrix |
| url | http://hdl.handle.net/10071/20172 |
| visible | 1 |