Determinants and inverses of circulant matrices with complex Fibonacci numbers

Abstract

Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.

Keywords

• Circulant matrix
• determinant
• complex Fibonacci sequence
• Fibonacci sequence
• Primary 15B05;15A15, Secondary 11B39