Equivalence Classes of Block Jacobi Matrices

A spectral equivalence for Jacobi matrices

We use the classical results of Baxter and Gollinski-Ibragimov to prove a new spectral equivalence for Jacobi matrices on l(N). In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences, and find necessary and sufficient conditions on the spectral measure such that ∑ ∞ k=n bk and ∑ ∞ k=n (a k − 1) lie in l 1 ∩ l .

Block Jacobi Matrices and Zeros of Multivariate Orthogonal Polynomials

A commuting family of symmetric matrices are called the block Jacobi matrices, if they are block tridiagonal. They are related to multivariate orthogonal polynomials. We study their eigenvalues and joint eigenvectors. The joint eigenvalues of the truncated block Jacobi matrices correspond to the common zeros of the multivariate orthogonal polynomials.

Two modified Jacobi methods for M-matrices

Rotation numbers for Jacobi matrices with matrix entries

A selfadjoined block tridiagonal matrix with positive definite blocks on the off-diagonals is by definition a Jacobi matrix with matrix entries. Transfer matrix techniques are extended in order to develop a rotation number calculation for its eigenvalues. This is a matricial generalization of the oscillation theorem for the discrete analogues of Sturm-Liouville operators. The three universality...

Centric connectivity index by shell matrices

Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topologi...