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

摘要

This article is an extension of the work [J. Rimas, On computing of arbitrary positive integer powers for one type of odd order diagonal matrices with zero row—I, Appl. Math. Comput., in press], in which the general expression of the lth power (l ∈ N) for one type of odd order tridiagonal matrices 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.