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:
“Every orientation presupposes a disorientation.”
—Hans Magnus Enzensberger (b. 1929)
“The true gardener then brushes over the ground with slow and gentle hand, to liberate a space for breath round some favourite; but he is not thinking about destruction except incidentally. It is only the amateur like myself who becomes obsessed and rejoices with a sadistic pleasure in weeds that are big and bad enough to pull, and at last, almost forgetting the flowers altogether, turns into a Reformer.”
—Freya Stark (1893–1993)