Circulant m-Diagonal Matrices Associated with Chebyshev Polynomials

In this study, we deal with an m banded circulant matrix, generally called circulant mdiagonal matrix. This special family of circulant matrices arise in many applications suchas prediction, time series analysis, spline approximation, difference solution of partialdifferential equations, and so on. We firstly obtain the statements of eigenvalues andeigenvectors of circulant m-diagonal matrix based on the Chebyshev polynomials of thefirst and second kind. Then we present an efficient formula for the integer powers of thismatrix family depending on the polynomials mentioned above. Finally, some illustrativeexamples are given by using maple software, one of computer algebra systems (CAS).