Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices
- Autores
- Tumpach, Alice Barbara; Larotonda, Gabriel Andrés
- Año de publicación
- 2024
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- This paper is a self-contained exposition of the geometry of symmetric positive-definitereal n×n matrices SPD(n), including necessary and sufficent conditions for a submanifold N ⊂ SPD(n) to be totally geodesic for the affine-invariant Riemannian metric.A non-linear projection x → π(x) on a totally geodesic submanifold is defined.This projection has the minimizing property with respect to the Riemannian metric:it maps an arbitrary point x ∈ SPD(n) to the unique closest element π(x) in thetotally geodesic submanifold for the distance defined by the affine-invariant Riemannian metric. Decompositions of the space SPD(n) follow, as well as variants of thepolar decomposition of non-singular matrices known as Mostow’s decompositions.Applications to decompositions of covariant matrices are mentioned.
Fil: Tumpach, Alice Barbara. University Of Lille.; Francia. Technische Universitat Wien; Austria
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina - Materia
-
MATRIX FACTORIZATION
NONPOSITIVE CURVATURE
SYMMETRIC POSITIVE-DEFINITE REAL MATRIX
TOTALLY GEODESIC - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/257863
Ver los metadatos del registro completo
id |
CONICETDig_b40b0ce52e90aacf672c52ef0a62deef |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/257863 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
network_name_str |
CONICET Digital (CONICET) |
spelling |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matricesTumpach, Alice BarbaraLarotonda, Gabriel AndrésMATRIX FACTORIZATIONNONPOSITIVE CURVATURESYMMETRIC POSITIVE-DEFINITE REAL MATRIXTOTALLY GEODESIChttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper is a self-contained exposition of the geometry of symmetric positive-definitereal n×n matrices SPD(n), including necessary and sufficent conditions for a submanifold N ⊂ SPD(n) to be totally geodesic for the affine-invariant Riemannian metric.A non-linear projection x → π(x) on a totally geodesic submanifold is defined.This projection has the minimizing property with respect to the Riemannian metric:it maps an arbitrary point x ∈ SPD(n) to the unique closest element π(x) in thetotally geodesic submanifold for the distance defined by the affine-invariant Riemannian metric. Decompositions of the space SPD(n) follow, as well as variants of thepolar decomposition of non-singular matrices known as Mostow’s decompositions.Applications to decompositions of covariant matrices are mentioned.Fil: Tumpach, Alice Barbara. University Of Lille.; Francia. Technische Universitat Wien; AustriaFil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaSpringer2024-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/257863Tumpach, Alice Barbara; Larotonda, Gabriel Andrés; Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices; Springer; Information Geometry; 7; S2; 11-2024; 913-9422511-24812511-249XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s41884-024-00146-zinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s41884-024-00146-zinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2405.20784info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:43:22Zoai:ri.conicet.gov.ar:11336/257863instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:43:22.937CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices |
title |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices |
spellingShingle |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices Tumpach, Alice Barbara MATRIX FACTORIZATION NONPOSITIVE CURVATURE SYMMETRIC POSITIVE-DEFINITE REAL MATRIX TOTALLY GEODESIC |
title_short |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices |
title_full |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices |
title_fullStr |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices |
title_full_unstemmed |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices |
title_sort |
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices |
dc.creator.none.fl_str_mv |
Tumpach, Alice Barbara Larotonda, Gabriel Andrés |
author |
Tumpach, Alice Barbara |
author_facet |
Tumpach, Alice Barbara Larotonda, Gabriel Andrés |
author_role |
author |
author2 |
Larotonda, Gabriel Andrés |
author2_role |
author |
dc.subject.none.fl_str_mv |
MATRIX FACTORIZATION NONPOSITIVE CURVATURE SYMMETRIC POSITIVE-DEFINITE REAL MATRIX TOTALLY GEODESIC |
topic |
MATRIX FACTORIZATION NONPOSITIVE CURVATURE SYMMETRIC POSITIVE-DEFINITE REAL MATRIX TOTALLY GEODESIC |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
This paper is a self-contained exposition of the geometry of symmetric positive-definitereal n×n matrices SPD(n), including necessary and sufficent conditions for a submanifold N ⊂ SPD(n) to be totally geodesic for the affine-invariant Riemannian metric.A non-linear projection x → π(x) on a totally geodesic submanifold is defined.This projection has the minimizing property with respect to the Riemannian metric:it maps an arbitrary point x ∈ SPD(n) to the unique closest element π(x) in thetotally geodesic submanifold for the distance defined by the affine-invariant Riemannian metric. Decompositions of the space SPD(n) follow, as well as variants of thepolar decomposition of non-singular matrices known as Mostow’s decompositions.Applications to decompositions of covariant matrices are mentioned. Fil: Tumpach, Alice Barbara. University Of Lille.; Francia. Technische Universitat Wien; Austria Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina |
description |
This paper is a self-contained exposition of the geometry of symmetric positive-definitereal n×n matrices SPD(n), including necessary and sufficent conditions for a submanifold N ⊂ SPD(n) to be totally geodesic for the affine-invariant Riemannian metric.A non-linear projection x → π(x) on a totally geodesic submanifold is defined.This projection has the minimizing property with respect to the Riemannian metric:it maps an arbitrary point x ∈ SPD(n) to the unique closest element π(x) in thetotally geodesic submanifold for the distance defined by the affine-invariant Riemannian metric. Decompositions of the space SPD(n) follow, as well as variants of thepolar decomposition of non-singular matrices known as Mostow’s decompositions.Applications to decompositions of covariant matrices are mentioned. |
publishDate |
2024 |
dc.date.none.fl_str_mv |
2024-11 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/257863 Tumpach, Alice Barbara; Larotonda, Gabriel Andrés; Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices; Springer; Information Geometry; 7; S2; 11-2024; 913-942 2511-2481 2511-249X CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/257863 |
identifier_str_mv |
Tumpach, Alice Barbara; Larotonda, Gabriel Andrés; Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices; Springer; Information Geometry; 7; S2; 11-2024; 913-942 2511-2481 2511-249X CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s41884-024-00146-z info:eu-repo/semantics/altIdentifier/doi/10.1007/s41884-024-00146-z info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2405.20784 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
_version_ |
1844613365549236224 |
score |
13.070432 |