Bezoutians of rational matrix functions, matrix equations and factorizations

AbstractThe notion of Bezoutian for a quadruple of rational matrix functions introduced by the authors in previous works is shown to be an adequate connecting link between certain factorization problems for rational matrix functions and quadratic and linear matrix equations. Particular attention is given to various types of coprime factorizations. A characterization of Bezoutians as angle operators between certain pairs of subspaces is also given