News Help Institutional access
Back to results
Bibliographic record · Consultation and access
Artículo

On the structure of the fundamental subspaces of acyclic matrices with in the diagonal

Jaume, Daniel Alejandro et al · American Journal of Combinatorics · 2023

Open-access full text
Quick overview. Review the resource’s basic details, then access the content using the main button. This page shows only the information needed to identify, cite, and open the work.
Author / responsible party
Jaume, Daniel Alejandro et al
Publisher
American Journal of Combinatorics
Year
2023
ISSN
2768-4202
ISSN
2768-4202
Language
English

Resource access

Open the content from the main option or choose another available source.

CONICET Digital CONICET Digital OAI-PMH
Entrar por CONICET Digital
Main access

Open-access full text

Texto completo identificado como acceso abierto.
Open text

Summary

Descripción general del contenido del recurso.

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

How to cite

Elegí el formato que necesitás y copiá la referencia al portapapeles.

APA 7

Jaume, D. A. E. A. (2023). On the structure of the fundamental subspaces of acyclic matrices with in the diagonal. http://hdl.handle.net/11336/233955

MLA

Jaume, Daniel Alejandro et al. "On the structure of the fundamental subspaces of acyclic matrices with in the diagonal." 2023. http://hdl.handle.net/11336/233955.

Chicago

Jaume, Daniel Alejandro et al. 2023. "On the structure of the fundamental subspaces of acyclic matrices with in the diagonal.". http://hdl.handle.net/11336/233955.

Harvard

Jaume, D. A. E. A. 2023, On the structure of the fundamental subspaces of acyclic matrices with in the diagonal, American Journal of Combinatorics, available at: http://hdl.handle.net/11336/233955 [Accessed 6 Aug. 2026].

Share and print

Save the record, copy its permanent link, or print it as a PDF.

Export reference

You can export the record in common formats for use in a reference manager.

RIS BibTeX

Resource details

Bibliographic information to help confirm that this is the correct material.

Title
On the structure of the fundamental subspaces of acyclic matrices with in the diagonal
Author / contributors
Jaume, Daniel Alejandro et al
Publisher
American Journal of Combinatorics
Publication year
2023
ISSN
2768-4202
ISSN
2768-4202
Language
English

Subjects

Explore related resources through these subjects.

ACYCLIC MATRIX; NULL SPACE BASIS; SPARSEST BASIS; RANK BASIS; TREE; https://purl.org/becyt/ford/1.1; https://purl.org/becyt/ford/1
Copied