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.
Read more about this topic: Orientation (geometry)
Famous quotes containing the words orientation and/or space:
“Institutions of higher education in the United States are products of Western society in which masculine values like an orientation toward achievement and objectivity are valued over cooperation, connectedness and subjectivity.”
—Yolanda Moses (b. 1946)
“Even the most subjected person has moments of rage and resentment so intense that they respond, they act against. There is an inner uprising that leads to rebellion, however short- lived. It may be only momentary but it takes place. That space within oneself where resistance is possible remains.”
—bell hooks (b. c. 1955)