In this posting the matrix is defined by where and are constant matrices.
The Baker–Campbell–Hausdorff theorem claims that:
where , and the lower-case letters and represent the adjoint actions of the corresponding matrices and (e.g. ).
One is frequently seeing the following series expression:
Source: T1269 = A.N.Richmond “Expansion for the exponential of a sum of matrices”; Int. Journal of Control (issue and year unknown).