On the norms of circulant matrices with the Fibonacci and Lucas numbers

On the Spectrum and Spectral Norms of r-Circulant Matrices with Generalized k-Horadam Numbers Entries

“…Our results generalize and improve the results in [1,2,4,5]. The following lemma can be found in [9], and we give a concise proof.…”

“…For example, Solak [1] established lower and upper bounds for the spectral norms of circulant matrices with Fibonacci and Lucas numbers entries. subsequently, Ipek [2] investigated some improved estimations for spectral norms of these matrices.…”

On the Bounds for the Norms of R-Circulant Matrices With the Jacobsthal and Jacobsthal Lucas Numbers

“…There have been several papers on the norms of special matrices [7][8][9][10]. Solak [8] has defined A = [a ij ] and B = [b ij ] as nxn circulant matrices, where a ij = F (mod(j−i,n)) and b ij = L (mod(j−i,n)) , then he has given some bounds for the A and B matrices concerned with the spectral and Eu-clidean norms. In (9) Shen, Cen found the bounds for the norms of r-circulant matrices with the Fibonocci and Lucas numbers.…”

Some norm inequalities for special Gram matrices

“…For example, Türkmen and Civciv have established some norm inequalities on circulant matrices with lucas numbers [1]. S.Solak has studied the norms of circulant matrices with bonacci and lucas numbers [2], Bozkurt and Tam have obtained some results belong to determinants and inverses of r-circulant matrices associated with a number sequence [3] and S.Shen and J.Cen have made a similar study by using the same special matrix with k-bonacci and k-lucas numbers [4]. For more properties, formulas belong to the Fibonacci, Lucas and Pell numbers (see, e.g., [11,12]).…”