On k-circulant matrices with the Lucas numbers

Let k be a nonzero complex number. In this paper, we determine the eigenvalues of a k-circulant matrix whose first row is (L1,L2,...,Ln), where Ln is the nth Lucas number, and improve the result which can be obtained from the result of Theorem 7. [28]. The Euclidean norm of such matrix is obtained. Bounds for the spectral norm of a k-circulant matrix whose first row is (L1^{-1},L2^{-1},...,Ln^{-1}) are also investigated. The obtained results are illustrated by examples.