Orientation (geometry) - Orientation of A Space

Orientation of A Space

The above described geometrical meaning of the word orientation should not be confused with its meaning in the context of linear algebra, where a different orientation means a change to the mirror image by a reflection.

Formally, for any dimension, the orientation of the image of an object under a direct isometry with respect to that object is the linear part of that isometry. Thus it is an element of SO(n), or, put differently, the corresponding coset in E+(n) / T, where T is the translation group.