Abstract
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 in principal and 1 , 1 , 1 , … , 1 in neighbouring diagonals – I, Applied Mathematics and Computation, 2006, doi:10.1016/j.amc.2006.10.022), in which the general expression of the lth power ( 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.
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