Definition: Define via product of exponentials .
Definition: Here “the bracket operator” is defined by following properties:
- if is homogeneous of the first degree,
- if is a rational number,
- for homogeneous in and of degree , i.e. .
Source: T1272 = W. Magnus “A Connection between the Baker-Hausdorff formula and a Problem of Burnside”; Annals of Mathematics; Vol 52, No 1, July 1950.
Related here: Magnus on matrix exponentials – https://eikonal.wordpress.com/2010/01/26/magnus-on-matrix-exponentials/