Full rank factorization in quasi-LDU form of totally nonpositive rectangular matrices

Let A = (a(ij)) is an element of R-nxm be a totally nonpositive matrix with rank(A) = r <= min{n, m} and a(11) = 0. In this paper we obtain a characterization in terms of the full rank factorization in quasi-LDU form, that is, A = (L) over tilde DU where (L) over tilde is an element of R-nxr...

Descripción completa

Detalles Bibliográficos
Autores: Cantó Colomina, Rafael|||0000-0002-1341-2800, Ricarte Benedito, Beatriz|||0000-0001-8094-1908, Urbano Salvador, Ana María|||0000-0001-8590-1243
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/52705
Acceso en línea:https://riunet.upv.es/handle/10251/52705
Access Level:acceso abierto
Palabra clave:LDU factorization
Echelon matrix
Totally nonpositive matrix
MATEMATICA APLICADA
Descripción
Sumario:Let A = (a(ij)) is an element of R-nxm be a totally nonpositive matrix with rank(A) = r <= min{n, m} and a(11) = 0. In this paper we obtain a characterization in terms of the full rank factorization in quasi-LDU form, that is, A = (L) over tilde DU where (L) over tilde is an element of R-nxr is a block lower echelon matrix, U is an element of R-rxm is a unit upper echelon totally positive matrix and D is an element of R-rxr is a diagonal matrix, with rank((L) over tilde) = rank(U) = rank(D) = r. We use this quasi-LDU decomposition to construct the quasi-bidiagonal factorization of A. Moreover, some properties about these matrices are studied. (C) 2013 Elsevier Inc. All rights reserved.