${\displaystyle Rot\underset{\_}{\underset{\_}{A}}:=\left\{\frac{\partial A_{\nu }}{\partial x_{\mu }}-\frac{\partial A_{\mu }}{\partial x_{\nu }}\right\}}$

where $\underset{\_}{\underset{\_}{A}}$ is an arbitrary four-vector

Note 1 to entry: Four-rotation is useful in STR. In general theory of relativity (GTR) for non-flat space-time, a more sophisticated method is used.

Note 2 to entry: Whereas three-dimensional rotation is described by a pseudovector, four-rotation is described by an antisymmetric four-dimensional tensor.

Note 3 to entry: In the International System of Quantities, the dimension of four-rotation is ${\mathrm{L}}^{-1}$.