Rotation matrix
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A rotation matrix is a matrix that generalizes the concept of a rotation of a set of points around a certain axis, about some arbitrary angle (or consequently rotating the axes about another axis).
For the former, in R3, the rotation about the x-axis is given by:
- <math>
\begin{pmatrix}
1 & 0 & 0 \\
0 & \cos{\theta} & \sin{\theta} \\
0 & - \sin{\theta} & \cos{\theta}
\end{pmatrix}
<math>
The rotation about the y-axis is given by:
- <math>
\begin{pmatrix}
\cos{\theta} & 0 & - \sin{\theta} \\
0 & 1 & 0 \\
\sin{\theta} & 0 & \cos{\theta}
\end{pmatrix}
<math>
The rotation about the z-axis is given by:
- <math>
\begin{pmatrix}
\cos{\theta} & -\sin{\theta} & 0 \\
\sin{\theta} & \cos{\theta} & 0 \\
0 & 0 & 1
\end{pmatrix}
<math>
with the equivalent clockwise rotation in R2 can be given from the minor M3,3 of the rotation about the z-axis.