Zu einem partiell differenzierbaren Vektorfeld

${\displaystyle G\colon U\longrightarrow \mathbb {R} ^{3}}$

auf einer offenen Teilmenge ${\displaystyle {}U\subseteq \mathbb {R} ^{3}}$ nennt man

${\displaystyle \operatorname {rot} _{}^{}{\left(G\right)}(P):={\begin{pmatrix}{\frac {\partial G_{3}}{\partial x_{2}}}(P)-{\frac {\partial G_{2}}{\partial x_{3}}}(P)\\{\frac {\partial G_{1}}{\partial x_{3}}}(P)-{\frac {\partial G_{3}}{\partial x_{1}}}(P)\\{\frac {\partial G_{2}}{\partial x_{1}}}(P)-{\frac {\partial G_{1}}{\partial x_{2}}}(P)\end{pmatrix}}}$

die Rotation von ${\displaystyle {}G}$.