Classical orthogonal polynomials and Leverrier-Faddeev algorithm for the matrix pencils sE-A

which, in general, is a strictly proper rational matrix (see [1, 5] and references therein). The computation of (sE−A)−1 can be carried out by using the Cramer rule, which requires the evaluation of n2 determinants of (n− 1)× (n− 1) polynomial matrices. Clearly, this is not a practical procedure for large n. We will describe an extension of the classical Leverrier-Faddeev algorithm using families of classical orthogonal polynomials following our previous contribution [2] when instead of a singular matrix E we used In. Here we generalize a recent result [6] based on the Chebyshev polynomials, a very