On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers

Abstract

-circulant matrices have applied in numerical computation, signal processing, coding theory, etc. In this study, our main goal is to investigate the r-circulant matrices of generalized Fermat numbers which are shown by We obtain the eigenvalues, determinants, sum identity of matrices. Also we find upper and lower bounds for the spectral norms of generalized Fermat r-circulant matrices. Beside these, we present 〖GR〗_(a,b,r)^* matrix in the form of the Hadamard product of two matrices as 〖GR〗_(a,b,r)^*=A.B. In addition, we get the right and skew-right circulant matrices for . Finally, we examine their different norms (Spectral and Euclidean) and limits for matrix norms.