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Hadamard functions of inverse M-Matrices

Claude Dellacherie·Servet Martinez·Jaime San Martin
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Abstract

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.

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Claude Dellacherie, Servet Martinez, Jaime San Martin. 2006-01-27. Hadamard functions of inverse M-Matrices. https://arxiv.org/abs/math/0601688

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