Involution exponential formula
= Involution exponential formula
{title2=$e^{-i\theta A}=\cos\theta\,I-i\sin\theta\,A$}
For a linear operator with $A^2=I$, every even power is $I$ and every odd power is $A$. Separating the absolutely convergent <matrix exponential> series into those powers proves the displayed identity without a Hermiticity assumption. If $A$ is also a <Hermitian operator>, the exponential is a <unitary operator>.