On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers

摘要

Let An=Circ(F1,F2,…,Fn) and Bn=Circ(L1,L2,…,Ln) be circulant matrices, where Fn is the Fibonacci number and Ln is the Lucas number. We prove that An is invertible for n > 2, and Bn is invertible for any positive integer n. Afterwards, the values of the determinants of matrices An and Bn can be expressed by utilizing only the Fibonacci and Lucas numbers. In addition, the inverses of matrices An and Bn are derived.