# I Exponential operators

1. Apr 28, 2016

### dyn

If I rearrange an equation invoving exponentials of operators and I take ex to the opposite side of the equation it becomes e-x. What happens if I try to take eA to the opposite side ? I know a exponential of operators can be expanded as a Taylor series which involves products of matrices but can this be inverted ?

2. Apr 28, 2016

### micromass

Staff Emeritus
Yes, $(e^{A})^{-1} = e^{-A}$

3. Apr 28, 2016

### dyn

Thanks. Are there any conditions for that to apply ? To invert an ordinary matrix requires a non-zero determinant. Are there any conditions on the operator/matrix in the exponential ? Also when taking the exponential over to the other side of the equation I presume order matters in case any operators do not commute ?

4. Apr 28, 2016

### micromass

Staff Emeritus
No. As long as $e^A$ exists (which it always does if $A$ is a bounded operator), then the above applies.

Yes.