On the structure of the fundamental subspaces of acyclic matrices with in the diagonal
- Autores
- Jaume, Daniel Alejandro; Pastine, Adrián Gabriel
- Año de publicación
- 2023
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- A matrix is called acyclic if replacing the diagonal entries with 0, and the nonzero diagonal entries with 1, yields the adjacency matrix of a forest. In this paper we show that the null space and the rank of an acyclic matrix with 0 in the diagonal is obtained from the null space and the rank of the adjacency matrix of the forest by multipliying by nonsingular diagonal matrices. We combine these with an algorithm for finding a sparsest basis of the null space of a forest to provide an optimal time algorithm for finding a sparsest basis of the null space of acyclic matrices with 0 in the diagonal.
Fil: Jaume, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina
Fil: Pastine, Adrián Gabriel. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina - Materia
-
ACYCLIC MATRIX
NULL SPACE BASIS
SPARSEST BASIS
RANK BASIS
TREE - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/233955
Ver los metadatos del registro completo
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On the structure of the fundamental subspaces of acyclic matrices with in the diagonalJaume, Daniel AlejandroPastine, Adrián GabrielACYCLIC MATRIXNULL SPACE BASISSPARSEST BASISRANK BASISTREEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A matrix is called acyclic if replacing the diagonal entries with 0, and the nonzero diagonal entries with 1, yields the adjacency matrix of a forest. In this paper we show that the null space and the rank of an acyclic matrix with 0 in the diagonal is obtained from the null space and the rank of the adjacency matrix of the forest by multipliying by nonsingular diagonal matrices. We combine these with an algorithm for finding a sparsest basis of the null space of a forest to provide an optimal time algorithm for finding a sparsest basis of the null space of acyclic matrices with 0 in the diagonal.Fil: Jaume, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; ArgentinaFil: Pastine, Adrián Gabriel. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaAmerican Journal of Combinatorics2023-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/233955Jaume, Daniel Alejandro; Pastine, Adrián Gabriel; On the structure of the fundamental subspaces of acyclic matrices with in the diagonal; American Journal of Combinatorics; American Journal of Combinatorics; 2; 8-2023; 39-582768-4202CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ajcombinatorics.org/Volume2/V2.03.pdfinfo:eu-repo/semantics/altIdentifier/url/https://ajcombinatorics.org/articles.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:34:22Zoai:ri.conicet.gov.ar:11336/233955instacron: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 09:34:22.678CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal |
| title |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal |
| spellingShingle |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal Jaume, Daniel Alejandro ACYCLIC MATRIX NULL SPACE BASIS SPARSEST BASIS RANK BASIS TREE |
| title_short |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal |
| title_full |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal |
| title_fullStr |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal |
| title_full_unstemmed |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal |
| title_sort |
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal |
| dc.creator.none.fl_str_mv |
Jaume, Daniel Alejandro Pastine, Adrián Gabriel |
| author |
Jaume, Daniel Alejandro |
| author_facet |
Jaume, Daniel Alejandro Pastine, Adrián Gabriel |
| author_role |
author |
| author2 |
Pastine, Adrián Gabriel |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
ACYCLIC MATRIX NULL SPACE BASIS SPARSEST BASIS RANK BASIS TREE |
| topic |
ACYCLIC MATRIX NULL SPACE BASIS SPARSEST BASIS RANK BASIS TREE |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
A matrix is called acyclic if replacing the diagonal entries with 0, and the nonzero diagonal entries with 1, yields the adjacency matrix of a forest. In this paper we show that the null space and the rank of an acyclic matrix with 0 in the diagonal is obtained from the null space and the rank of the adjacency matrix of the forest by multipliying by nonsingular diagonal matrices. We combine these with an algorithm for finding a sparsest basis of the null space of a forest to provide an optimal time algorithm for finding a sparsest basis of the null space of acyclic matrices with 0 in the diagonal. Fil: Jaume, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina Fil: Pastine, Adrián Gabriel. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina |
| description |
A matrix is called acyclic if replacing the diagonal entries with 0, and the nonzero diagonal entries with 1, yields the adjacency matrix of a forest. In this paper we show that the null space and the rank of an acyclic matrix with 0 in the diagonal is obtained from the null space and the rank of the adjacency matrix of the forest by multipliying by nonsingular diagonal matrices. We combine these with an algorithm for finding a sparsest basis of the null space of a forest to provide an optimal time algorithm for finding a sparsest basis of the null space of acyclic matrices with 0 in the diagonal. |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023-08 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/233955 Jaume, Daniel Alejandro; Pastine, Adrián Gabriel; On the structure of the fundamental subspaces of acyclic matrices with in the diagonal; American Journal of Combinatorics; American Journal of Combinatorics; 2; 8-2023; 39-58 2768-4202 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/233955 |
| identifier_str_mv |
Jaume, Daniel Alejandro; Pastine, Adrián Gabriel; On the structure of the fundamental subspaces of acyclic matrices with in the diagonal; American Journal of Combinatorics; American Journal of Combinatorics; 2; 8-2023; 39-58 2768-4202 CONICET Digital CONICET |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/url/https://ajcombinatorics.org/Volume2/V2.03.pdf info:eu-repo/semantics/altIdentifier/url/https://ajcombinatorics.org/articles.html |
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American Journal of Combinatorics |
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American Journal of Combinatorics |
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