Polynomials that preserve nonnegative monomial matrices

Abstract: A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we provide a formula for computing an arbitrary power of a monomial matrix and a formula for computing the polynomial of a nonnegative monomial matrix.

Keywords: Polynomial; Nonnegative matrix; Monomial matrix