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

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

There are also particular definitions on the following entries:

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