2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107735We prove that the class of GUM matrices is the largest class of bi-potential matrices stable under Hadamard increasing functions. We also show that any power greater than 1, in the sense of Hadamard functions, of an inverse M-matrix is also inverse M-matrix showing a conjecture stated in Neumann 1998. We study the class of filtered matrices, which include naturally the GUM matrices, and present some sufficient conditions for a filtered matrix to be a bi-potential.Probability15A48, 15A51, 60J45text