On computing of arbitrary positive integer powers for one type of tridiagonal matrices of even order

This paper is an extension of the work [On computing of arbitrary positive integer powers for one type of tridiagonal matrices, Applied Mathematics and Computation, to appear], in which the general expression of the lth power (l ∈ N) for one type of tridiagonal matrices of order n = 2p + 1 (p ∈ N) is presented. In this new paper we derive the general expression of the lth power (l ∈ N) for the same type of tridiagonal matrices of order n = 2p (p ∈ N). Expressions of eigenvectors and Jordan's form of the matrix, and of transforming matrix and its inverse are given, too.