Isolated and structured families of models for stochastic symmetric matrices
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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/20.500.12207/6246 |
Resumo: | Stochastic symmetric matrices with a dominant eigenvalue, ,can be written as the sum of λt (where λ is the first eigenvalue), with a symmetric error matrix E. The information in the stochastic matrix will be condensed in its structured vectors, λ, and the sum of square of residues, V. When the matrices of a family correspond to the treatments of a base design, we say the family is structured. The action of the factors, which are considered in the base design, on the structure vectors of the family matrices will be analyzed. We use ANOVA (Analysis of Variance) and related techniques, to study the action under linear combinations of the components of structure vectors of the m matrices of the model. Orthogonal models with m treatments are associated to orthogonal partitions. The hypothesis to be tested, on the action of the factors in the base design, will be associated to the spaces in the orthogonal partitions.We will show how to carry out transversal and longitudinal analysis for families of stochastic symmetric matrices with dominant eigenvalue associated to orthogonal models. |
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Isolated and structured families of models for stochastic symmetric matricesBase designModelsStructured familiesSymmetric stochastic matrixStochastic symmetric matrices with a dominant eigenvalue, ,can be written as the sum of λt (where λ is the first eigenvalue), with a symmetric error matrix E. The information in the stochastic matrix will be condensed in its structured vectors, λ, and the sum of square of residues, V. When the matrices of a family correspond to the treatments of a base design, we say the family is structured. The action of the factors, which are considered in the base design, on the structure vectors of the family matrices will be analyzed. We use ANOVA (Analysis of Variance) and related techniques, to study the action under linear combinations of the components of structure vectors of the m matrices of the model. Orthogonal models with m treatments are associated to orthogonal partitions. The hypothesis to be tested, on the action of the factors in the base design, will be associated to the spaces in the orthogonal partitions.We will show how to carry out transversal and longitudinal analysis for families of stochastic symmetric matrices with dominant eigenvalue associated to orthogonal models.Wiley2024-03-12T11:02:05Z2021-11-01T00:00:00Z2021-112023-06-24T09:17:30Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/20.500.12207/6246eng2577-74082-s2.0-85123622759P-00T-FDHWOS:000746924300061cv-prod-2983351https://doi.org/10.1002/cmm4.1152Dias, CristinaSantos, CarlaMexia, João Tiagoinfo: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:RCAAP2024-03-14T20:59:43Zoai:repositorio.ipbeja.pt:20.500.12207/6246Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T04:00:58.738325Repositório 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 |
Isolated and structured families of models for stochastic symmetric matrices |
title |
Isolated and structured families of models for stochastic symmetric matrices |
spellingShingle |
Isolated and structured families of models for stochastic symmetric matrices Dias, Cristina Base design Models Structured families Symmetric stochastic matrix |
title_short |
Isolated and structured families of models for stochastic symmetric matrices |
title_full |
Isolated and structured families of models for stochastic symmetric matrices |
title_fullStr |
Isolated and structured families of models for stochastic symmetric matrices |
title_full_unstemmed |
Isolated and structured families of models for stochastic symmetric matrices |
title_sort |
Isolated and structured families of models for stochastic symmetric matrices |
author |
Dias, Cristina |
author_facet |
Dias, Cristina Santos, Carla Mexia, João Tiago |
author_role |
author |
author2 |
Santos, Carla Mexia, João Tiago |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Dias, Cristina Santos, Carla Mexia, João Tiago |
dc.subject.por.fl_str_mv |
Base design Models Structured families Symmetric stochastic matrix |
topic |
Base design Models Structured families Symmetric stochastic matrix |
description |
Stochastic symmetric matrices with a dominant eigenvalue, ,can be written as the sum of λt (where λ is the first eigenvalue), with a symmetric error matrix E. The information in the stochastic matrix will be condensed in its structured vectors, λ, and the sum of square of residues, V. When the matrices of a family correspond to the treatments of a base design, we say the family is structured. The action of the factors, which are considered in the base design, on the structure vectors of the family matrices will be analyzed. We use ANOVA (Analysis of Variance) and related techniques, to study the action under linear combinations of the components of structure vectors of the m matrices of the model. Orthogonal models with m treatments are associated to orthogonal partitions. The hypothesis to be tested, on the action of the factors in the base design, will be associated to the spaces in the orthogonal partitions.We will show how to carry out transversal and longitudinal analysis for families of stochastic symmetric matrices with dominant eigenvalue associated to orthogonal models. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-11-01T00:00:00Z 2021-11 2023-06-24T09:17:30Z 2024-03-12T11:02:05Z |
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/20.500.12207/6246 |
url |
http://hdl.handle.net/20.500.12207/6246 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2577-7408 2-s2.0-85123622759 P-00T-FDH WOS:000746924300061 cv-prod-2983351 https://doi.org/10.1002/cmm4.1152 |
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 |
Wiley |
publisher.none.fl_str_mv |
Wiley |
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 |
repository.mail.fl_str_mv |
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1799138183996243968 |