On k-circulant matrices involving the Jacobsthal-Lucas numbers

Abstract

In this paper, we consider a $k$-circulant matrix involving the Jacobsthal-Lucas numbers where $k$ is a nonzero complex number. Then we obtain the formulae for the eigenvalues of such matrix improving the result in [Y. Yazlik and N. Taskara, On the norms of an $r$-circulant matrix with the generalized $k$-Horadam numbers, J. Inequal. Appl. 2013]. We show that in some cases the result given in the same paper can not be applied to the determinant of such matrix. The norms of such matrix are determined, and the bounds for the spectral norm of a $k$-circulant matrix involving the inverses of the Jacobsthal-Lucas numbers are also investigated. Finally, the obtained results are illustrated by examples.

Keywords

• k-circulant matrix
• Jacobsthal - Lucas numbers
• eigenvalues
• norms of a matrix

References

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