On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-II

摘要

This paper is an extension of the work (J. Rimas, On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-I, Appl. Math. Comput., in press), 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 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.