 An actual "differential rotation", or "infinitesimal rotation matrix" has the form
where is vanishingly small and , for instance with ,

The computation rules are as usual except that infinitesimals of second order are routinely dropped.With these rules, these matrices do not satisfy all the same properties as ordinary finite rotation matrices under the usual treatment of infinitesimals.It turns out that "the order in which infinitesimal rotations are applied is irrelevant".