Generalized companion matrices and matrix representations for generalized Bezoutians

AbstractA generalization of companion matrices is presented as the starting point for developing a unified algebraic method to get matrix representations for generalized Bezoutians. Special cases are discussed. In particular, well-known formulas for Hankel and Toeplitz Bezoutians are obtained; also, new matrix representations are given, for example in a basis of orthogonal polynomials, using corresponding Christoffel-Darboux formulas