The Hadamard core of the totally nonnegative matrices Original Research Article

An m-by-n matrix A is called totally nonnegative if every minor of A is nonnegative. The Hadamard product of two matrices is simply their entry-wise product. 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–nonzero patterns for which all totally nonnegative matrices lie in this class; and connections to Oppenheimʹs inequality.