Infinitesimal unitary transformation ($U(ϵ)=I+iϵF+O({ϵ}^2)$)

Differentiating a unitary operator family at the identity gives an anti-Hermitian tangent. In the convention $U(ϵ)=I+iϵF+O({ϵ}^2)$ for real $ϵ$, the generator $F$ is Hermitian. This is the one-parameter version of the Hermitian quantum generator convention. A finite linear truncation need not itself be exactly unitary.