Characterization of symmetric \(M\)-matrices as resistive inverses

DOI10.1016/j.laa.2008.10.027zbMath1165.15019OpenAlexW2017587938MaRDI QIDQ999811

J. M. Gesto, Andrés M. Encinas, Ángeles Carmona, Enrique Bendito

Publication date: 10 February 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.10.027

zbMATH Keywords

Schrödinger operatorsMoore-Penrose inverse\(M\)-matricesKirchhoff indexeffective resistanceGreen kernelsirreducible Stieltjes matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (16)

Resistance distances on networks ⋮ Potential theory on finite networks ⋮ The Kirchhoff index of unicycle weighted chains ⋮ Boundary Value Problems on Finite Networks ⋮ The Kirchhoff indexes of some composite networks ⋮ Discrete elliptic operators and their Green operators ⋮ Eigenvalues with respect to a weight for general boundary value problems on networks ⋮ A combinatorial expression for the group inverse of symmetric \(M\)-matrices ⋮ Kirchhoff indexes of a network ⋮ Generalized inverses of symmetric \(M\)-matrices ⋮ Resistance distances in extended or contracted networks ⋮ Unnamed Item ⋮ Green matrices associated with generalized linear polyominoes ⋮ Green's function in partial subdivision networks ⋮ The Kirchhoff indices of join networks ⋮ Group inverse matrix of the normalized Laplacian on subdivision networks

Cites Work

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• On Euclidean distance matrices
• Some characterizations of symmetric inverse \(M\)-matrices
• Description of the sub-Markov kernel associated to generalized ultrametric matrices. An algorithmic approach
• Inverse \(M\)-matrix inequalities and generalized ultrametric matrices
• Generalized ultrametric matrices -- a class of inverse \(M\)-matrices
• Ultrametric matrices and induced Markov chains
• Potential theory for Schrödinger operators on finite networks
• Special Ultrametric Matrices and Graphs
• Inverse of Strictly Ultrametric Matrices are of Stieltjes Type
• A Linear Algebra Proof that the Inverse of a Strictly Ultrametric Matrix is a Strictly Diagonally Dominant Stieltjes Matrix
• Distances in Weighted Trees and Group Inverse of Laplacian Matrices
• The M-Matrix Group Generalized Inverse Problem for Weighted Trees
• Minimizing Effective Resistance of a Graph
• Generalized inverse of the Laplacian matrix and some applications
• Inequalities and equalities associated with the Campbell-Youla generalized inverse of the indefinite admittance matrix of resistive networks

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