Positive integer powers of complex symmetric circulant matrices

Abstract

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 circ n ( 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.