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

Year 2023, , 956 - 964, 18.10.2023

Bahar Kuloǧlu , Engin Eser , Engin Özkan

https://doi.org/10.16984/saufenbilder.1280572

Cited By: 1

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.

Keywords

Fermat number, generalized Fermat numbers, norm (spectral and Euclidean), eigenvalues, circulant matrices

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