Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars
Autor(a) principal: | |
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Data de Publicação: | 2010 |
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/10400.26/46822 |
Resumo: | In this paper on space geometry, generalized inverses are used in the study of distances. Three cases are considered: distance from a point to a plane, distance from a point to a line and distance between two skew lines. Moore-Penrose inverses occur in the expressions of the feet of the perpendiculars and in the representation of the vectors materializing the distances. The results of this kind of problems fit in the cadre of approximation theory and, because best approximation problems often require the projection of the origin onto linear varieties, in order to solve the proposed problems, we make extensive use of the conjugacy principle, much present in Mathematics. The obtained results are not only useful for undergraduate Science and Engineering students but are also applicable in very practical sciences and techniques, notably on Coordinate Metrology, Photogrammetry, etc. Moreover, this paper could pave the way for more generalized problems demanding more sophisticated approaches. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Conjugacy and geometry II : moore-penrose inverse and feet of the perpendicularsIn this paper on space geometry, generalized inverses are used in the study of distances. Three cases are considered: distance from a point to a plane, distance from a point to a line and distance between two skew lines. Moore-Penrose inverses occur in the expressions of the feet of the perpendiculars and in the representation of the vectors materializing the distances. The results of this kind of problems fit in the cadre of approximation theory and, because best approximation problems often require the projection of the origin onto linear varieties, in order to solve the proposed problems, we make extensive use of the conjugacy principle, much present in Mathematics. The obtained results are not only useful for undergraduate Science and Engineering students but are also applicable in very practical sciences and techniques, notably on Coordinate Metrology, Photogrammetry, etc. Moreover, this paper could pave the way for more generalized problems demanding more sophisticated approaches.Pushpa Publishing HouseRepositório ComumCosta, C.Martins, Fernando M. L.Serôdio, RogérioTadeu, PedroVincente, M. A. FacasVitória, José2023-09-28T09:58:33Z20102010-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.26/46822enginfo: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:RCAAP2023-10-05T02:15:49Zoai:comum.rcaap.pt:10400.26/46822Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:33:18.905561Repositório 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 |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars |
title |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars |
spellingShingle |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars Costa, C. |
title_short |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars |
title_full |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars |
title_fullStr |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars |
title_full_unstemmed |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars |
title_sort |
Conjugacy and geometry II : moore-penrose inverse and feet of the perpendiculars |
author |
Costa, C. |
author_facet |
Costa, C. Martins, Fernando M. L. Serôdio, Rogério Tadeu, Pedro Vincente, M. A. Facas Vitória, José |
author_role |
author |
author2 |
Martins, Fernando M. L. Serôdio, Rogério Tadeu, Pedro Vincente, M. A. Facas Vitória, José |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Repositório Comum |
dc.contributor.author.fl_str_mv |
Costa, C. Martins, Fernando M. L. Serôdio, Rogério Tadeu, Pedro Vincente, M. A. Facas Vitória, José |
description |
In this paper on space geometry, generalized inverses are used in the study of distances. Three cases are considered: distance from a point to a plane, distance from a point to a line and distance between two skew lines. Moore-Penrose inverses occur in the expressions of the feet of the perpendiculars and in the representation of the vectors materializing the distances. The results of this kind of problems fit in the cadre of approximation theory and, because best approximation problems often require the projection of the origin onto linear varieties, in order to solve the proposed problems, we make extensive use of the conjugacy principle, much present in Mathematics. The obtained results are not only useful for undergraduate Science and Engineering students but are also applicable in very practical sciences and techniques, notably on Coordinate Metrology, Photogrammetry, etc. Moreover, this paper could pave the way for more generalized problems demanding more sophisticated approaches. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010 2010-01-01T00:00:00Z 2023-09-28T09:58:33Z |
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/10400.26/46822 |
url |
http://hdl.handle.net/10400.26/46822 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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 |
Pushpa Publishing House |
publisher.none.fl_str_mv |
Pushpa Publishing House |
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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1799133598345854976 |