es

This section is divided into a number of subsections, links to which are:

Rotations

2D Rotations

3D Rotations

Euler Theorem

Quaternions

 

Compositions

Reflections are the elements of the orthogonal group O(n) whose canonical form is
\[ \begin{bmatrix} -1 & {\bf 0} \\ \phantom{-}0 & {\bf I} \end{bmatrix} , \]
where I is the (n − 1) × (n − 1) identity matrix, and the zeros denote row or column zero matrices. In other words, a reflection is a transformation that transforms the space in its mirror image with respect to a hyperplane.

In dimension two, every rotation can be decomposed into a product of two reflections. More precisely, a rotation of angle θ is the product of two reflections whose axes form an angle of θ / 2.


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