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)
“I would have broke mine eye-strings, cracked them, but
To look upon him, till the diminution
Of space had pointed him sharp as my needle;
Nay, followed him till he had melted from
The smallness of a gnat to air, and then
Have turned mine eye and wept.”
—William Shakespeare (1564–1616)