Hadamard Functions of Inverse M-Matrices

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 α ≥ 1, in the sense of Hadamard functions, of an inverseM -matrix is also inverseM matrix showing a conjecture stated in Neumann [15]. 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. AMS subject classification: 15A48, 15A51, 60J45.