LAUSR

Let k be a nonzero complex number. In this paper, we consider a k-circulant matrix whose first row is $$(P_{1},P_{2},\dots ,P_{n})$$(P1,P2,⋯,Pn), where $$P_{n}$$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 $$(P_{1}^{-1},P_{2}^{-1},\dots ,P_{n}^{-1})$$(P1-1,P2-1,⋯,Pn-1) are also investigated. The obtained results are illustrated by examples.