Hadamard Products of Stable Polynomials Are Stable

A real polynomial is asymptotically.stable when all of its zeros lie in the open left half of the complex plane. We show that the Hadamard coefficient-wise. product of two stable polynomials is again stable, improving upon some known results. Via the associated Hurwitz matrices we find another example of a class of totally nonnegative matrices which is closed under Hadamard multiplication