  We 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.
