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:
“Much of what passes for quality on British television is no more than a reflection of the narrow elite which controls it and has always thought that its tastes were synonymous with quality.”
—Rupert Murdoch (b. 1931)
“Their bodies are buried in peace; but their name liveth for evermore.”
—Apocrypha. Ecclesiasticus, 44:14.
The line “their name liveth for evermore” was chosen by Rudyard Kipling on behalf of the Imperial War Graves Commission as an epitaph to be used in Commonwealth War Cemeteries. Kipling had himself lost a son in the fighting.
“It was the most ungrateful and unjust act ever perpetrated by a republic upon a class of citizens who had worked and sacrificed and suffered as did the women of this nation in the struggle of the Civil War only to be rewarded at its close by such unspeakable degradation as to be reduced to the plane of subjects to enfranchised slaves.”
—Anna Howard Shaw (1847–1919)