Clusters of point matrices

Clusters of point matrices In this paper, in addition to classical orthogonal polynomials, we introduce the orthogonal polynomials of degree $n-1$ at $n$ points. They result from interpolational polynomials. The name "point matrices" is justified by the fact that we do not consider a class of similar or congruent matrices that play the key role in a linear space and connected with its bases. We consider matrices with a fixed set of nodes (or points) $x_1,\dots,x_n$. A certain matrix cluster corresponds to each set of nodes. A simple connection between eigenproblems of the Hunkel matrix $H$ and the symmetric Jacjbi matrix $T$ has been obtained.