Rotation matrix

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.

See also

Template:Math-stubde:Rotationsmatrix

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