Positive integer powers of certain tridiagonal matrices and corresponding anti-tridiagonal matrices (Q2166700)

Summary: In this paper, we firstly derive a general expression for the entries of the \(m\) th \((m\in\mathbb{N})\) power for two certain types of tridiagonal matrices of arbitrary order. Secondly, we present a method for computing the positive integer powers of the anti-tridiagonal matrix corresponding to these matrices. Also, we give Maple 18 procedures in order to verify our calculations.