Inversion With Respect To The Origin
Inversion with respect to the origin corresponds to additive inversion of the position vector, and also to scalar multiplication by −1. The operation commutes with every other linear transformation, but not with translation: it is in the central of the general linear group. "Inversion" without indicating "in a point", "in a line" or "in a plane", means this inversion; in physics 3-dimensional reflection through the origin is also called a parity transformation.
In mathematics, reflection through the origin refers to the point reflection of Euclidean space Rn across the origin of the Cartesian coordinate system. Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by, and can also be written as, where is the identity matrix. In three dimensions, this sends, and so forth.
Read more about this topic: Point Reflection
Famous quotes containing the words respect and/or origin:
“Art, in the artist, is proportion, or, a habitual respect to the whole by an eye loving beauty in details. And the wonder and charm of it is the sanity in insanity which it denotes.”
—Ralph Waldo Emerson (1803–1882)
“All good poetry is the spontaneous overflow of powerful feelings: it takes its origin from emotion recollected in tranquillity.”
—William Wordsworth (1770–1850)