Coordinate system

One of the main points in linear algebra is the ability to change coordinate system. Whatever we do, it is good to do it in the right coordinate system, where things are easier. For example, a rotation about the z-axes in three dimensional space is given by

| cos(t)   sin(t)   0|
| -sin(t)  cos(t)   0|
|   0        0      1|

If we want to rotate about an other axes, then we just use a suitable coordinate system in which the transformation matrix looks as above.

This was using some creative commons povray code by Gilles Tran who authored it in 2000-2004. Quicktime (.m4v) version of the above Gif.