Some results on geometric circulant matrices involving the Leonardo numbers

Abstract

In this study, by the motivation of the papers in the literature, we construct a special geometric circulant matrix $Le_{r^*}$ whose entries are the Leonardo numbers. Then, we investigate some linear algebraic properties of these matrices. More specifically, we present some bounds for the spectral norm, as well as Euclidean norm of this matrix form. For this purpose, we benefit from the spectacular properties of the Leonardo numbers. Furthermore, we throw light on the obtained results with examples. In addition to all these, we give two Matlab code in order to calculate the results related norms more easily and more accurately in a short time in the computer environment.