On the bounds for the norms of r-circulant matrices with the Fibonacci and Lucas numbers

In this paper, we have found upper and lower bounds for the spectral norms of r-circulant matrices in the forms A = Cr(F0, F1, …, Fn−1), B = Cr(L0, L1, …, Ln−1), and we have obtained some bounds for the spectral norms of Kronecker and Hadamard products of A and B matrices.