Rotation

Rotation occurs about an axis. Rotation contrasts with Translation in discussions of motion. The convention is for rotations to be counterclockwise.

Rotation also appears in Symmetry Operations.

For 2D, (x,y), the matrix for a counterclockwise rotation of \theta is the following:

\begin{bmatrix} cos \theta && - sin \theta \\ sin \theta && cos \theta\end{bmatrix}

For a rotation in 3D, (x,y,z) counterclockwise by angle \theta about the z-axis, the matrix is the following:

\begin{bmatrix} cos \theta && - sin \theta && 0 \\ sin \theta && cos \theta && 0 \\ 0 && 0 && 1 \end{bmatrix}