Reflection Across A Line in The Plane
Reflection across a line through the origin in two dimensions can be described by the following formula
Where v denotes the vector being reflected, l denotes any vector in the line being reflected in, and v·l denotes the dot product of v with l. Note the formula above can also be described as
Where the reflection of line l on a is equal to 2 times the projection of v on line l minus v. Reflections in a line have the eigenvalues of 1, and −1.
Read more about this topic: Reflection (mathematics)
Famous quotes containing the words reflection, line and/or plane:
“Water. Its sunny track in the plain; its splashing in the garden canal, the sound it makes when in its course it meets the mane of the grass; the diluted reflection of the sky together with the fleeting sight of the reeds; the Negresses fill their dripping gourds and their red clay containers; the song of the washerwomen; the gorged fields the tall crops ripening.”
—Jacques Roumain (1907–1945)
“Expediency of literature, reason of literature, lawfulness of writing down a thought, is questioned; much is to say on both sides, and, while the fight waxes hot, thou, dearest scholar, stick to thy foolish task, add a line every hour, and between whiles add a line.”
—Ralph Waldo Emerson (1803–1882)
“with the plane nowhere and her body taking by the throat
The undying cry of the void falling living beginning to be something
That no one has ever been and lived through screaming without enough air”
—James Dickey (b. 1923)