Duality: the states | ψn ) and polynomials Qn (u)

Besides the signal points {c_n}, the key ingredients of spectral analysis are the Lanczos coupling constants {α_n, β_n}. They are defined in terms of the elements of the basis set of the Lanczos state vectors. The duality, i.e. Lanczos dual representation {| ψn), Q_n(u)} enables switching from the work with the Lanczos state vectors to the analysis with the Lanczos polynomials. A change from one representation to the other is readily accomplished.