Abstract
Given a polynomial f of degree n , we denote by C its companion matrix, and by S the truncated shift operator of order n . We consider Lyapunov-type equations of the form X − SXC => W and X − CXS = W . We derive some properties of these equations which make it possible to characterize Bezoutian matrices as solutions of the first equation with suitable right-hand sides W (similarly for Hankel and the second equation) and to write down explicit expressions for these solutions. This yields explicit factorization formulae for polynomials in C , for the Schur-Cohn matrix, and for matrices satisfying certain intertwining relations, as well as for Bezoutian matrices.
Published Version
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