Path product matrices and eventually inverse M-matrices

摘要

Those nonnegative matrices, some Hadamard power of which are inverse M-matrices, are characterized. This requires a refinement of the strict path product necessary condition [ C. R. Johnson and R. L. Smith, Linear Multilinear Algebra, 46 ( 1999), pp. 177 - 191] for an inverse M-matrix. The smallest such Hadamard power may be arbitrarily large. It is also shown that, beyond some threshold, all continuous Hadamard powers of an inverse M-matrix are inverse M. In the process, several new results about inverse M-matrices are given.