The Lanczos finite-dimensional linear vector space ℒM

This chapter deals with the Lanczos finite-dimensional linear vector space. The Lanczos vector space can be defined through its basis and the appropriate scalar product. A finite sequence of the Lanczos orthogonal polynomials of the first kind is complete. Since the polynomials {Q_n(u)} have no multiple zeros, all the spectral representations of functions in L_M will exhibit only simple poles.