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:
“But before the extremity of the Cape had completely sunk, it appeared like a filmy sliver of land lying flat on the ocean, and later still a mere reflection of a sand-bar on the haze above. Its name suggests a homely truth, but it would be more poetic if it described the impression which it makes on the beholder.”
—Henry David Thoreau (1817–1862)
“Next to the originator of a good sentence is the first quoter of it. Many will read the book before one thinks of quoting a passage. As soon as he has done this, that line will be quoted east and west.”
—Ralph Waldo Emerson (1803–1882)
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