A sufficient condition for a non-negative matrix to have non-negative determinant

It is shown that a matrix with non-negative entries has non-negative determinant if in each row the elements decrease, by steadily smaller amounts, as one proceeds (in either direction) away from the main diagonal. This condition suffices to establish non- negativity of the determinant for certain matrices to which the familiar Minkowski- Hadamard-Ostrowski dominance conditions do not apply. In the symmetric case it provides a sufficient condition for non-negative definiteness. This may be applied to establish the positive definiteness of certain real symmetric Toeplitz matrices.