Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices

Abstract

It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between left circulant, $g$-circulant matrices and circulant matrix, the invertibility of Tribonacci left circulant and Tribonacci $g$-circulant matrices is also discussed. Finally, the determinants and inverse matrices of these matrices are given, respectively.