The Hadamard core of the totally nonnegative matrices

An m-by-n matrix A is called totally nonnegative if every minor of A is non negative. The Hadamard product of two matrices is simply their entry-wise p roduct, This paper introduces the subclass of totally nonnegative matrices whose Hadamard product with any totally nonnegative matrix is again totally nonnegative, Many properties concerning this class are discussed including : a complete characterization for min{m, n} < 4; a characterization of the zero-non-zero patterns for which all totally nonnegative matrices lie in th is class; and connections to Oppenheim's inequality, <(c)> 2001 Elsevier Sc ience Inc, All rights reserved.