On the Determinants of Complex-Valued Fibonacci Circulant Matrices

Abstract

Circulant matrices are interesting due to their rich algebraic structures and various applications. Fibonacci circulant matrices, circulant matrices whose first row is a list of consecutive Fibonacci numbers, have been studied since 1970. In this paper, the notions of complex-valued Fibonacci circulant matrices are introduced. The explicit formula for the determinant of such matrices are completely determined. Known results on the determinants of Fibonacci circulant matrices can be viewed as special cases. At the end, some open problems are discussed.