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

In this paper, firstly we derive a general expression for the mth power (m ∈ N) for one type of tridiagonal matrices of even order. Secondly we present a method for computing integer powers of the antitridiagonal matrices that is corresponding with these matrices. Then, we present some examples to illustrate our results and give Maple 18 procedure in order to verify our calculations.