Analyzing Chebyshev polynomial-based geometric circulant matrices

Abstract

<p>This paper explores geometric circulant matrices whose entries are Chebyshev polynomials of the first or second kind. Motivated by our previous research on $ r- $circulant matrices and Chebyshev polynomials, we focus on calculating the Frobenius norm and deriving estimates for the spectral norm bounds of these matrices. Our analysis reveals that this approach yields notably improved results compared to previous methods. To validate the practical significance of our research, we apply it to existing studies on geometric circulant matrices involving the generalized $ k- $Horadam numbers. The obtained results confirm the effectiveness and utility of our proposed approach.</p>