The m th Power of an$n \times n$ Matrix and the Bell Polynomials
Jean L. Lavoie · SIAM Journal on Applied Mathematics · 1975
It is common knowledge that the mth power for $m\geqq n$ of an n-square matrix A can be represented as a linear combination of the lower powers of A. We show that the coefficients in this linear combination can be expressed in terms of the well-known Bell polynomials.