On the norms of another form of r-circulant matrices with the hyper-fibonacci and lucas numbers

In this paper, we compute the spectral norms of r− circulant matrices with the hyper-Fibonacci and hyper-Lucas numbers of the forms Fr = Circ − r(F (0) k , F (1) k , . . . , F (n−1) k ), Lr = Circ − r(L (0) k , L (1) k , . . . , L (n−1) k ) and their Hadamard and Kronecker products. For this, we firstly compute the spectral and Euclidean norms of circulant matrices of the forms F = Circ(F (0) k , F (1) k , . . . , F (n−1) k ) and L = Circ(L (0) k , L (1) k , . . . , L (n−1) k ). Moreover, we give some examples related to special cases of our results