Abstract :
We conjecture that for an n × n matrix A which is an inverse of an M-matrix, the Hadamard product A ring operator A is also an inverse of an M-matrix. We have checked this conjecture without failure on many many examples. But here we show that for quite a few well known classes of inverses of M-matrices, the conjecture is true. It is known that the more general conjecture, that when A and B are n × n inverses of M-matrices, then A ring operator B is also an inverse of an M-matrix, is false. However, here too we are able to display some classes of inverses of M-matrices which are closed under taking Hadamard products.
