Invertibility and explicit inverses of circulant-type matrices with \(k\)-Fibonacci and \(k\)-Lucas numbers (Q1722405)

Summary: 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 [\textit{S.-Q. Shen} et al., Appl. Math. Comput. 217, No. 23, 9790--9797 (2011; Zbl 1222.15010)].