A note on matrices involving the Chebyshev polynomials

Abstract

In this talk, we establish a connection between some classical topics in applied mathematics - circulant matrices and the Chebyshev polynomials. First, we define circulant matrices whose entries are the Chebyshev polynomials of the first or second kind and examine their basic properties. Then we determine the bounds of the norms of such matrices. It turns out that the obtained results can be seen as the unification and generalization of many previously obtained results on circulant matrices involving the generalized Horadam numbers. We point out one direction of applications, but it is clear that there are many possibilities. With appropriate modifications, these results can be applied in different areas, such as - statistics, data approximation, interpolation, engineering, economics, signal and image processing, numerical analysis, physics and error correcting code theory, to name but a few.