dc.contributor.author Bendito Pérez, Enrique dc.contributor.author Carmona Mejías, Ángeles dc.contributor.author Encinas Bachiller, Andrés Marcos dc.contributor.author Gesto Beiroa, José Manuel dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III dc.date.accessioned 2007-08-01T19:30:23Z dc.date.available 2007-08-01T19:30:23Z dc.date.issued 2007-01-25 dc.identifier.uri http://hdl.handle.net/2117/1168 dc.description.abstract We aim here at characterizing those nonnegative matrices whose inverse is an irreducible Stieltjes matrix. Specifically, we prove that any irreducible Stieltjes matrix is a resistive inverse. To do that we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite Schrödinger operator which ground state is determined by the its lowest eigenvalue and the corresponding positive eigenvector. We also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric M-matrices. The key tool is the definition of the effective resistance with respect to a nonnegative value and a weight. We prove that these effective resistances verify similar properties to those satisfied by the standard effective resistances which leads us to carry out an exhaustive analysis of the generalized inverses of singular irreducible symmetric M-matrices. Moreover we pay special attention on those generalized inverses identified with Green operators, which in particular includes the analysis of the Moore-Penrose inverse. dc.format.extent 29 p. dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 2.5 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/2.5/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Matrices dc.subject.other Schrödinger operator dc.subject.other M-matrices dc.subject.other generalized inverses dc.subject.other Green kernels dc.subject.other Moore-Penrose inverse dc.subject.other effective resistance dc.subject.other Kirchhoff index dc.title Characterization of symmetric M-matrices as resistive inverses dc.type Article dc.subject.lemac Matriu S, Teoria dc.contributor.group Universitat Politècnica de Catalunya. VARIDIS - Varietats Riemannianes Discretes i Teoria del Potencial dc.subject.ams Classificació AMS::15 Linear and multilinear algebra; matrix theory dc.rights.access Open Access dc.relation.projectidctt BFM2003-06014 local.personalitzacitacio true
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