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:
“A little reflection will enable any person to detect in himself that setness in trifles which is the result of the unwatched instinct of self-will and to establish over himself a jealous guardianship.”
—Harriet Beecher Stowe (1811–1896)
“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)
“As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the plane at the base of a mountain, instead of climbing steadily to its top.”
—Henry David Thoreau (1817–1862)