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)
“It is a great many years since at the outset of my career I had to think seriously what life had to offer that was worth having. I came to the conclusion that the chief good for me was freedom to learn, think, and say what I pleased, when I pleased. I have acted on that conviction... and though strongly, and perhaps wisely, warned that I should probably come to grief, I am entirely satisfied with the results of the line of action I have adopted.”
—Thomas Henry Huxley (1825–95)
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—Friedrich Nietzsche (1844–1900)