Some explicit formulas for the polynomial decomposition of the matrix exponential and applications Original Research Article

This paper is devoted to the study of some formulas for polynomial decomposition of the exponential of a square matrix A. More precisely, we suppose that the minimal polynomial MA(X) of A is known and has degree m. Therefore, etA is given in terms of P0(A),…,Pm−1(A), where the Pj(A) are polynomials in A of degree less than m, and some explicit analytic functions. Examples and applications are given. In particular, the two cases m=5 and m=6 are considered.