Glossary Canonical realization: A state-space realization that has specific properties that makes it unique. Characteristic polynomial: The scalar denominator of a transfer function. Column-reduced: A polynomial matrix with non-singular column leading coefficient matrix. Coprime: See relatively prime. Denominator polynomial: The polynomial appearing in the denominator of a rational transfer fun...

We apply and extend some well known and some recent tech niques from algebraic residue theory in order to relate to each other two major subjects of algebraic and numerical computing that is computa tions with structured matrices and solving a system of polynomial equa tions In the rst part of our paper we extend the Toeplitz and Hankel structures of matrices and some of their known properties ...

Spectral properties of special matrices matrices have been widely applied. We focus on monomial matrices over a finite field Fp, p 6= 2. We describe a way to find the minimal annihilating polynomial, a set of linearly independent eigenvectors.

For all hyperbolic polynomials we proved in [11] a Lipschitz estimate of Jacobi matrices built by orthogonalizing polynomials with respect to measures in the orbit of classical Perron-Frobenius-Ruelle operators associated to hyperbolic polynomial dynamics (with real Julia set). Here we prove that for all sufficiently hyperbolic polynomials this estimate becomes exponentially better when the dim...

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasise...

We study the invertibility of M -variate polynomial (respectively : Laurent polynomial) matrices of size N by P . Such matrices represent multidimensional systems in various settings including filter banks, multipleinput multiple-output systems, and multirate systems. Given an N × P polynomial matrix H(z) of degree at most k, we want to find a P × N polynomial (resp. : Laurent polynomial) left ...