| dc.contributor.author | Casanellas Rius, Marta |
| dc.contributor.author | Fernández Sánchez, Jesús |
| dc.contributor.author | Roca Lacostena, Jordi |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| dc.date.accessioned | 2022-04-22T06:45:29Z |
| dc.date.available | 2022-04-23T00:32:08Z |
| dc.date.issued | 2020-12-17 |
| dc.identifier.citation | Casanellas, M.; Fernández-Sánchez, J.; Roca, J. An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator. "Linear and multilinear algebra", 17 Desembre 2020, p. 1-12. |
| dc.identifier.issn | 0308-1087 |
| dc.identifier.uri | http://hdl.handle.net/2117/366197 |
| dc.description.abstract | A Markov matrix is embeddable if it can represent a homogeneous continuous-time Markov process. It is well known that if a Markov matrix has real and pairwise-different eigenvalues, then the embeddability can be determined by checking whether its principal logarithm is a rate matrix or not. The same holds for Markov matrices that are close enough to the identity matrix. In this paper we exhibit open sets of Markov matrices that are embeddable and whose principal logarithm is not a rate matrix, thus proving that the principal logarithm test above does not suffice generically. |
| dc.description.sponsorship | All authors are partially funded by AGAUR Project 2017 SGR-932 and MINECO/FEDER Projects MTM2015-69135 and MDM-2014-0445. J. Roca-Lacostena has received also funding from Secretaria d'Universitats i Recerca de la Generalitat de Catalunya (AGAUR 2018FI_B_00947) and European Social Funds. |
| dc.format.extent | 12 p. |
| dc.language.iso | eng |
| dc.publisher | Taylor & Francis |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica |
| dc.subject.lcsh | Algebras, Linear |
| dc.subject.lcsh | Multilinear algebra |
| dc.subject.lcsh | Matrices |
| dc.subject.lcsh | Markov processes |
| dc.subject.other | Markov matrix |
| dc.subject.other | Markov generator |
| dc.subject.other | Embedding problem |
| dc.subject.other | Rate identifiability |
| dc.title | An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator |
| dc.type | Article |
| dc.subject.lemac | Àlgebra lineal |
| dc.subject.lemac | Àlgebra multilineal |
| dc.subject.lemac | Matrius (Àlgebra) |
| dc.subject.lemac | Markov, Processos de |
| dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
| dc.identifier.doi | 10.1080/03081087.2020.1854165 |
| dc.subject.ams | Classificació AMS::15 Linear and multilinear algebra; matrix theory |
| dc.subject.ams | Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes |
| dc.relation.publisherversion | https://www.tandfonline.com/doi/abs/10.1080/03081087.2020.1854165 |
| dc.rights.access | Open Access |
| local.identifier.drac | 30660673 |
| dc.description.version | Postprint (author's final draft) |
| local.citation.author | Casanellas, M.; Fernández-Sánchez, J.; Roca, J. |
| local.citation.publicationName | Linear and multilinear algebra |
| local.citation.startingPage | 1 |
| local.citation.endingPage | 12 |
