A generalized bezoutian matrix
M. J. C. Gover, Stephen Mark Barnett · Linear and Multilinear Algebra · 1990
Bezoutian matrices play an important role in linear systems theory, providing iinks between such topics as controllability and observability, canonical forms, realization, root location for polynomials, and Hankel matrices. Like the usual bezoutian matrix, the proposed generalized bezoutian, termed the conjugate-bezoutian, is defined in terms of two polynomials. It is shown that some ol the properties and applications of the standard case extend to this new matrix. I hese include a generalization of a related Sylvester matrix, a companion matrix formula, and expression of the inverse of the conjugate bezoutian in a generalized Hankel matrix form.