Editing Matrix exponential (section)

=== The Baker–Campbell–Hausdorff formula ===
In the other direction, if {{mvar|X}} and {{mvar|Y}} are sufficiently small (but not necessarily commuting) matrices, we have
<math display="block">e^Xe^Y = e^Z,</math>
where {{mvar|Z}} may be computed as a series in [[commutator]]s of {{mvar|X}} and {{mvar|Y}} by means of the [[Baker–Campbell–Hausdorff formula]]:<ref>{{harvnb|Hall|2015}} Chapter 5</ref>
<math display="block">Z = X + Y + \frac{1}{2}[X,Y] + \frac{1}{12}[X,[X,Y]] - \frac{1}{12}[Y,[X,Y]]+ \cdots,</math>
where the remaining terms are all iterated commutators involving {{mvar|X}} and {{mvar|Y}}. If {{mvar|X}} and {{mvar|Y}} commute, then all the commutators are zero and we have simply {{math|1=''Z'' = ''X'' + ''Y''}}.