orthogonal

The word orthogonal comes from the Greek orthe and gonia, or “right angle.” It was originally used as synonym of perpendicular. This is where the use of “orthogonal” in orthogonal lines, orthogonal circles, and other geometric terms come from.

In the realm of linear algebra, two vectors are orthogonal when their dot product is zero, which gave rise a generalization of two vectors on some inner product space (not necessarily dot product) being orthogonal when their inner product is zero.

There are also particular definitions on the following entries:

• orthogonal matrices

• orthogonal polynomials

• orthogonal vectors

In a more broad sense, it can be said that two objects are orthogonal if they do not “coincide” in some way.

Title	orthogonal
Canonical name	Orthogonal
Date of creation	2013-03-22 12:07:30
Last modified on	2013-03-22 12:07:30
Owner	akrowne (2)
Last modified by	akrowne (2)
Numerical id	13
Author	akrowne (2)
Entry type	Definition
Classification	msc 51F20
Classification	msc 65F25
Classification	msc 15A63
Classification	msc 05E35
Classification	msc 42C05
Classification	msc 33C45
Classification	msc 15A57