On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers

Abstract

In this paper, we compute the spectral norms of r− circulant matrices with the hyper-Fibonacci and hyper-Lucas numbers of the forms) and their Hadamard and Kronecker products. For this, we firstly compute the spectral and Euclidean norms of circulant matrices of the forms. Moreover, we give some examples related to special cases of our results.

Hybrid hyper-Fibonacci and hyper-Lucas numbers

“…Some combinatorial identities of a new generalization of the hyper-Lucas numbers are obtained in [3]. In [5], the authors considered 𝑟-circulant matrices with the hyper-Fibonacci and the hyper-Lucas numbers and calculated the spectral norms of these matrices.…”

Genelleştirilmiş tetranacci sayıları ile tanımlı circulant matrislerin özdeğerleri

“…For instance, Kocer et al (Kocer et al, 2007) have studied the norms of circulant matrices which terms are Horadam numbers. In (Shen and Cen, 2010), Shen and Cen have obtained the bounds for the norms of −circulant matrices Bahsi in (Bahşi, 2015) has computed norms of circulant matrices with the generalized Fibonacci and Lucas numbers.…”

“…In (Tuglu and Kızılateş, 2015a;Kızılateş and Tuglu, 2016;Kızılateş and Tuglu, 2018), Tuglu and Kızılateş have given some matrix norms of circulant, −circulant and geometric circulant matrices with the special Fibonacci numbers. Also, Bahşi calculated the matrix norms of circulant matrices with Tribonacci sequence (Bahşi, 2015).…”

The Spectral Norm of a Circulant Matrix

“…Bahşi [1] have already studied this question. We will survey their results in Section 2 and give further results in Sections 3 and 4.…”