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)
“The parent must not give in to his desire to try to create the child he would like to have, but rather help the child to develop—in his own good time—to the fullest, into what he wishes to be and can be, in line with his natural endowment and as the consequence of his unique life in history.”
—Bruno Bettelheim (20th century)
“At the moment when a man openly makes known his difference of opinion from a well-known party leader, the whole world thinks that he must be angry with the latter. Sometimes, however, he is just on the point of ceasing to be angry with him. He ventures to put himself on the same plane as his opponent, and is free from the tortures of suppressed envy.”
—Friedrich Nietzsche (1844–1900)