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:
“In the last analysis, love is only the reflection of a man’s own worthiness from other men.”
—Ralph Waldo Emerson (1803–1882)
“The line of separation was very distinct, and the Indian immediately remarked, “I guess you and I go there,—I guess there’s room for my canoe there.” This was his common expression instead of saying “we.” He never addressed us by our names, though curious to know how they were spelled and what they meant, while we called him Polis. He had already guessed very accurately at our ages, and said that he was forty-eight.”
—Henry David Thoreau (1817–1862)
“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)