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

AbstractThis 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