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

Authors : Mustafa BAHŞİ, Süleyman SOLAK

Pages : 76-85

Doi:10.47000/tjmcs.715052

View : 17 | Download : 13

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :In this paper, we compute the spectral norms of $r-$ circulant matrices with the hyper-Fibonacci and hyper-Lucas numbers of the forms $F_{r}=Circ-rinsert ignore into journalissuearticles values(F_k^{insert ignore into journalissuearticles values(0);},F_k^{insert ignore into journalissuearticles values(1);},...,F_k^{insert ignore into journalissuearticles values(n-1);}); $ ,  $L_r=Circ-rinsert ignore into journalissuearticles values(L_{k}^{\leftinsert ignore into journalissuearticles values( 0\right); },L_{k}^{\leftinsert ignore into journalissuearticles values( 1\right); },...,L_{k}^{\leftinsert ignore into journalissuearticles values( n-1\right); });$  and their Hadamard and Kronecker products. For this, we firstly compute the spectral and Euclidean norms of circulant matrices of the forms $F=Circinsert ignore into journalissuearticles values(F_{k}^{\leftinsert ignore into journalissuearticles values( 0\right); }, F_{k}^{\leftinsert ignore into journalissuearticles values( 1\right); },... ,F_{k}^{\leftinsert ignore into journalissuearticles values( n-1\right); });$ and $L=Circinsert ignore into journalissuearticles values(L_{k}^{\leftinsert ignore into journalissuearticles values( 0\right); },L_{k}^{\leftinsert ignore into journalissuearticles values( 1\right); },...,L_{k}^{\leftinsert ignore into journalissuearticles values( n-1\right); });$. Moreover, we give some examples related to special cases of our results.
Keywords : Circulant matrix, r circulant matrix, hyper Fibonacci numbers, hyper Lucas numbers, Euclidean norm, spectral norm