Rotation matrix

A rotation matrix is an orthogonal n x n matrix having a determinant equal to 1.

The linear transformation T(x) = A x is a "rotation".

In two dimensions a rotation by <math>\theta</math> can be represented by the matrix:

<math> R = \begin{pmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{pmatrix}</math>