Polynomials and Hankel matrices (Q1061191)

Compatibility of a Hankel \(n\times n\)-matrix H and a polynomial f of degree m, \(m\leq n\), is defined. If \(m=n\), compatibility means that \(HC^ T_ f=C_ fH\) where \(C_ f\) is the companion matrix of f. The latter concept is generalized to the case that \(m<n\) by requiring \(H\Gamma^ T_ f=\Gamma_ fH\). Here \(\Gamma_ f\) is an \(n\times n\)-matrix depending only on the polynomial f.