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 (L-1 , L-2 , . . , L-n ), where L n 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 (L-1(-1) , L2, . . . , -1L (-1)(n) ) are also investigated. The obtained results are illustrated by examples.