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)
“The limitless future of childhood shrinks to realistic proportions, to one of limited chances and goals; but, by the same token, the mastery of time and space and the conquest of helplessness afford a hitherto unknown promise of self- realization. This is the human condition of adolescence.”
—Peter Blos (20th century)