Polynomials and Hankel matrices. (English) Zbl 0569.15005

Fiedler, Miroslav

Linear Algebra Appl. 66, 235-248 (1985).

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.

Reviewer: J.de Graaf

MSC:

15A21

Canonical forms, reductions, classification

Keywords:

Hankel matrix; compatibility; companion matrix

References:

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