A note on new inner-matrix for stability

In this note a new inner-matrix for stability is introduced. The application of such a matrix for open left half-plane and inside the unit circle roots of complex polynomials is shown. Furthermore, the Hurwitz minors for left half-plane stability of real polynomial are given in terms of inners determinants of a resultant matrix. This connection is obtained by symmetrizing the Schur-Complement of the resultant (innerwise) matrix.