Positive integer powers of complex symmetric circulant matrices

In [J. Rimas, On computing of arbitrary positive integer powers for one type of odd order symmetric circulant matrices - I, Applied Mathematics and Computation 165 (2005) 137-141; J. Rimas, On computing of arbitrary positive integer powers for one type of even order symmetric circulant matrices - I, Applied Mathematics and Computation 172 (2006) 86-90], Rimas derived a general expression for the entries of the qth power (q∈N) of the n×n real symmetric circulant matrix circn(0,1,0,0,…,0,0,1) for all n∈N. In this paper, we present an extension of that interesting work, deriving a similar expression for the entries of the positive integer powers of any complex symmetric circulant matrix.