On computing of arbitrary positive integer powers for tridiagonal matrices with elements 1, 0, 0, … , 0, 1 in principal and 1, 1, 1, … , 1 in neighbouring diagonals – II

摘要

This paper is an extension of the work [J. Rimas, On computing of arbitrary positive integer powers for tridiagonal matrices with elements 1, 0, 0, … , 0, 1 in principal and 1, 1, 1, … , 1 in neighbouring diagonals – I, Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2006.07.145], in which the general expression of the lth power (l ∈ N) for one type of tridiagonal matrices of arbitrary order is given. In this new paper, we present the complete derivation of this general expression. Expressions of eigenvectors of the matrix and of the transforming matrix and its inverse are given, too.