On k-circulant matrices involving the Pell numbers

Let k be a nonzero complex number. In this paper, we consider a k-circulant matrix whose first row is (P1,P2,…,Pn), where Pn is the nth Pell number, and obtain the formulae for the eigenvalues of such matrix improving the result which can be obtained from the result of Theorem 7 (Yazlik and Taskara in J Inequal Appl 2013:394, 2013). The obtained formulae for the eigenvalues of a k-circulant matrix involving the Pell numbers show that the result of Theorem 6 (Jiang et al. in WSEAS Trans Math 12(3):341–351, 2013) [i.e. Theorem 8 (Yazlik and Taskara in J Inequal Appl 2013:394, 2013)] is not always applicable. The Euclidean norm of such matrix is determined. The upper and lower bounds for the spectral norm of a k-circulant matrix whose first row is (P1^{-1},P2^{-1},…,Pn^{-1}) are also investigated. The obtained results are illustrated by examples.