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On the bounds for the norms of \(r\)-circulant matrices with the Fibonacci and Lucas numbers. (English) Zbl 1211.15029

Let \((F_n)\) and \((L_n)\) be the Fibonacci and Lucas numbers. Let \(A=C_r(F_0,F_1,\ldots,F_{n-1})\) and \(B=C_r(L_0,L_1,\ldots,L_{n-1})\) be \(r\)-circulant matrices. The authors give lower and upper bounds for the spectral norms of these matrices and obtain some for the spectral norms of Hadamard and Kronecker products of these matrices.

MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
Full Text: DOI

References:

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