On k-circulant matrices with the Lucas numbers

Abstract

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 n^{th} Lucas number, and improve the result which can be obtained from the result of Theorem 7. [25]. The Euclidean norm of such matrix is obtained. Bounds for the spectral norm of the Hadamard inverse of such matrix are also investigated. The obtained results are illustrated by examples.