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dc.contributor.authorBendito Pérez, Enrique
dc.contributor.authorCarmona Mejías, Ángeles
dc.contributor.authorEncinas Bachiller, Andrés Marcos
dc.contributor.authorGesto Beiroa, José Manuel
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.description.abstractWe 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.extent29 p.
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.otherSchrödinger operator
dc.subject.othergeneralized inverses
dc.subject.otherGreen kernels
dc.subject.otherMoore-Penrose inverse
dc.subject.othereffective resistance
dc.subject.otherKirchhoff index
dc.titleCharacterization of symmetric M-matrices as resistive inverses
dc.subject.lemacMatriu S, Teoria
dc.contributor.groupUniversitat Politècnica de Catalunya. VARIDIS - Varietats Riemannianes Discretes i Teoria del Potencial
dc.subject.amsClassificació AMS::15 Linear and multilinear algebra; matrix theory
dc.rights.accessOpen Access

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Attribution-NonCommercial-NoDerivs 2.5 Spain
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