%0 Journal Article %1 Bendito20091336 %A Bendito, E. %A Carmona, A. %A Encinas, A. M. %A Gesto, J. M. %D 2009 %J Linear Algebra and its Applications %K effective.resistance graph.theory m-matrix matrix network resistor %N 4 %P 1336--1349 %R 10.1016/j.laa.2008.10.027 %T Characterization of symmetric M-matrices as resistive inverses %V 430 %X 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 this we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite Schrödinger operator whose ground state is determined by the lowest eigenvalue of the matrix 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.

@article{Bendito20091336, 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 this we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite Schrödinger operator whose ground state is determined by the lowest eigenvalue of the matrix 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. }, added-at = {2016-05-23T07:59:49.000+0200}, author = {Bendito, E. and Carmona, A. and Encinas, A. M. and Gesto, J. M.}, biburl = {https://www.bibsonomy.org/bibtex/2175aa521ceb205effbdc22654ba6366b/ytyoun}, doi = {10.1016/j.laa.2008.10.027}, interhash = {ba72b2e432525e3c51b48f0c7afd2f80}, intrahash = {175aa521ceb205effbdc22654ba6366b}, issn = {0024-3795}, journal = {Linear Algebra and its Applications }, keywords = {effective.resistance graph.theory m-matrix matrix network resistor}, number = 4, pages = {1336--1349}, timestamp = {2016-05-23T08:00:10.000+0200}, title = {Characterization of symmetric {M}-matrices as resistive inverses }, volume = 430, year = 2009 }