# Product of Matrix exponential?

1. Apr 1, 2014

### dipole

Is there an expression, in general, for the product of two matrix exponentials, for non-commuting matrices?

i.e. something of the form,
$$e^Ae^B = e^{( * )}$$

where the ( * ) would, I assume, depend in some way on the commutator $[A,B]$?

I can only find examples online when $[A,B] = 0$ which is rather trivial, but nothing about the more general case...

2. Apr 1, 2014