Editing Matrix exponential (section)

==== Using the Jordan–Chevalley decomposition ====
By the [[Jordan–Chevalley decomposition]], any <math>n \times n</math> matrix ''X'' with complex entries can be expressed as
<math display="block">X = A + N </math>
where
* ''A'' is diagonalizable
* ''N'' is nilpotent
* ''A'' [[commutativity|commutes]] with ''N''

This means that we can compute the exponential of ''X'' by reducing to the previous two cases:
<math display="block">e^X = e^{A+N} = e^A e^N. </math>

Note that we need the commutativity of ''A'' and ''N'' for the last step to work.