Symmetric factorizations and localization of zeroes of rational matrix functions

Abstract

Symmetric factorizations of self-adjoint rational matrix functions are studied using the concent of Bezoutian for rational matrix functions as the main tool. In particular, the distribution of zeroes of a rational matrix function F(λ) is described in terms of inertia of the Bezoutian corresponding to symmetric factorizations of . Symmetric factorizations are constructed so that F(λ) and G(λ) are coprime in a certain sense.

¹Partially supported by the fund for promotion of research at the Technion-Israel Institute of Technology.

¹Partially supported by the fund for promotion of research at the Technion-Israel Institute of Technology.

Notes

¹Partially supported by the fund for promotion of research at the Technion-Israel Institute of Technology.