On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order—II

摘要

This paper is an extension of the work [J. Rimas, On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order—I, Applied Mathematics and Computation, in press], in which the general expression of the lth power (l ∈ N) for one type of symmetric tridiagonal matrices of order n = 2p + 1 (p ∈ N) is given. In this new paper, we present the complete derivation of this general expression. Expressions of eigenvectors and Jordan’s form of the matrix and of the transforming matrix and its inverse are given, too.