Editing Transformation matrix (section)

===Rotation===

For [[coordinate rotation|rotation]] by an angle θ '''counterclockwise''' (positive direction) about the origin the functional form is <math>x' = x \cos \theta - y \sin \theta</math> and <math>y' =  x \sin \theta + y \cos \theta</math>.  Written in matrix form, this becomes:<ref>{{Cite web | url=http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec03.pdf | title=Lecture Notes | website=ocw.mit.edu | access-date=2024-07-28}}</ref>
<math display="block">\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos \theta & -\sin\theta \\ \sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}</math>

Similarly, for a rotation '''clockwise''' (negative direction) about the origin, the functional form is <math>x' = x \cos \theta + y \sin \theta</math> and <math>y' = -x \sin \theta + y \cos \theta</math> the matrix form is:
<math display="block">\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos \theta &   \sin\theta \\ -\sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}</math>

These formulae assume that the ''x'' axis points right and the ''y'' axis points up.