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:
“Public morning diversions were the last dissipating habit she obtained; but when that was accomplished, her time was squandered away, the power of reflection was lost, [and] her ideas were all centered in dress, drums, routs, operas, masquerades, and every kind of public diversion. Visionary schemes of pleasure were continually present to her imagination, and her brain was whirled about by such a dizziness that she might properly be said to labor under the distemper called the vertigo.”
—Sarah Fielding (1710–1768)
“I thank heaven for a man like Adolf Hitler, who built a front line of defense against the anti-Christ of Communism.”
—Frank Buchman (1878–1961)
“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)