The linear algebra of a generalized Tribonacci matrix

In this paper, we consider a generalization of a regular Tribonacci matrix for two variables and show that it can be factorized by some special matrices. We produce several new interesting identities and find an explicit formula for the inverse and k−th power. We also give a relation between the matrix and a matrix exponential of a special matrix.

Keywords:

Tribonacci sequence, factorization of matrices, matrix exponential matrix inverse,

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