The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g -Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers

Abstract

Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and $g$-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant and $g$-circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant and $g$-circulant matrices by utilizing the relationship between left circulant, $g$-circulant matrices and circulant matrix, respectively.