Lanczos polynomials matrix

The Jacobi matrix and the Lanczos polynomial matrix within... 

This is the orthogonality relation of the two Lanczos polynomials Q (m) and Qm(u) with the weight function, which is the residue dk [48]. We recall that the sequence Q = (Q ( z-) coincides with the set of eigenvectors of the Jacobi matrix (60). 

Matrix elements of the evolution operator in terms of the Lanczos polynomials... 

The recursion (84) can be extended to operators and matrices. This is done by using the Cayley-Hamilton theorem [2], which states that for a given analytic scalar function/(m), the expression for its operator counterpart/(U) is obtained via replacement of u by U as in Eq. (6). In this way, we can introduce the Lanczos operator and matrix polynomials defined by the following recursions ... 

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