# Simple examples of $3 \times 3$ rotation matrices

I'd like to have some numerically simple examples of $3 \times 3$ rotation matrices that are easy to handle in hand calculations (using only your brain and a pencil). Matrices that contain too many zeros and ones are boring, and ones with square roots are undesirable. A good example is something like $$M = \frac19 \begin{bmatrix} 1 & -4 & 8 \\ 8 & 4 & 1 \\ -4 & 7 & 4 \end{bmatrix}$$ Does anyone have any other examples, or a process for generating them?

One general formula for a rotation matrix is given here. So one possible approach would be to choose $u_x$, $u_y$, $u_z$ and $\theta$ so that you get something simple. Simple enough for hand calculations, but not trivial. Like the example given above.

• rotation matrix you meant?ok there is examples en.wikipedia.org/wiki/Rotation_matrix Dec 15 '13 at 8:06