Hadamard Functions of Inverse M -Matrices
Claude Dellacherie, Servet Martı́nez, Jaime San Martı́n · SIAM Journal on Matrix Analysis and Applications · 2009
We prove that the class of generalized ultrametric matrices (GUM) is the largest class of bipotential matrices stable under Hadamard increasing functions. We also show that any power $\alpha\ge1$, in the sense of Hadamard functions, of an inverse M-matrix is also inverse M-matrix. This was conjectured for $\alpha=2$ by Neumann in [Linear Algebra Appl., 285 (1998), pp. 277–290], and solved for integer $\alpha\ge1$ by Chen in [Linear Algebra Appl., 381 (2004), pp. 53–60]. 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 bipotential.