# Exponential operators

• I
• dyn

#### 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 ?

Yes, ##(e^{A})^{-1} = e^{-A}##

• yungboss
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 ?

Thanks. Are there any conditions for that to apply ?

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

Also when taking the exponential over to the other side of the equation I presume order matters in case any operators do not commute ?

Yes.

• dyn