Explicit form of the inverse matrices of tribonacci circulant type matrices. (English) Zbl 1383.15028

Summary: 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.


15B05 Toeplitz, Cauchy, and related matrices
15B36 Matrices of integers
15A09 Theory of matrix inversion and generalized inverses
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