Invertibility and Explicit Inverses of Circulant-Type Matrices with k -Fibonacci and k -Lucas Numbers

Abstract

Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant-type matrices with the $k$-Fibonacci and $k$-Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which generalizes the results in Shen et al. (2011).