ABSTRACT

This chapter deals with the completeness proof for the Lanczos polynomials. It presents the original Christoffel-Darboux formula which includes only the polynomials of the first kind. The chapter proves that eigenvectors of the J-matrix form an orthonormal complete set of vectors and, hence, represent a basis set. Orthonormality is a matter of convenience, but completeness is essential both in theory and in practice.