On computing of arbitrary positive integer powers for tridiagonal matrices with elements -1,0,0,…,0,1-1,0,0,…,0,1 in principal and 1,1,1,…,11,1,1,…,1 in neighbouring diagonals – II

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,…,0,1-1,0,0,…,0,1 in principal and 1,1,1,…,11,1,1,…,1 in neighbouring diagonals – I, Applied Mathematics and Computation, 2006, http://dx.doi.org/10.1016/j.amc.2006.10.022), in which the general expression of the l  th power (l∈N)l∈N) for one type of tridiagonal matrices of arbitrary order n(n∈N,n⩾2) 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.