A property concerning the Hadamard powers of inverse M-matrices Original Research Article

The main result of this paper is the following: if A=(aij) is an inverse M-matrix, A(k)=(aijk) denotes the kth Hadamard power of A, then A(k) is an inverse M-matrix for any positive integer k>1. In the case k=2, this settles a conjecture of Neumann [Linear Algebra Appl. 285 (1998) 278] affirmatively.