# orthogonal

## orthogonal

[awr-thog-uh-nl]
1.
Mathematics.
a.
Also, pertaining to or involving right angles or perpendiculars: an orthogonal projection.
b.
(of a system of real functions) defined so that the integral of the product of any two different functions is zero.
c.
(of a system of complex functions) defined so that the integral of the product of a function times the complex conjugate of any other function equals zero.
d.
(of two vectors) having an inner product equal to zero.
e.
(of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
f.
(of a square matrix) defined so that its product with its transpose results in the identity matrix.
2.
Crystallography. referable to a rectangular set of axes.

Origin:
1565–75; obsolete orthogon(ium) right triangle (< Late Latin orthogōnium < Greek orthogṓnion (neuter) right-angled, equivalent to ortho- ortho- + -gōnion -gon) + -al1

orthogonality, noun
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
 orthogonal (ɔːˈθɒɡənəl) —adj 1. relating to, consisting of, or involving right angles; perpendicular 2. maths a.  (of a pair of vectors) having a defined scalar product equal to zero b.  (of a pair of functions) having a defined product equal to zero or'thogonally —adv

Collins English Dictionary - Complete & Unabridged 10th Edition
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Etymonline
Word Origin & History

orthogonal
from Fr. orthogonal, from orthogone, from L.L. orthogonius, from Gk. orthogonios "right-angled," from ortho- "straight" (see ortho-) + gonia "angle," related to gony "knee" (see knee).
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
 orthogonal   (ôr-thŏg'ə-nəl)  Pronunciation Key  Relating to or composed of right angles. Relating to a matrix whose transpose equals its inverse. Relating to a linear transformation that preserves the length of vectors.
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FOLDOC
Computing Dictionary

### orthogonal definition

geometry
At 90 degrees (right angles).
N mutually orthogonal vectors span an N-dimensional vector space, meaning that, any vector in the space can be expressed as a linear combination of the vectors. This is true of any set of N linearly independent vectors.
The term is used loosely to mean mutually independent or well separated. It is used to describe sets of primitives or capabilities that, like linearly independent vectors in geometry, span the entire "capability space" and are in some sense non-overlapping or mutually independent. For example, in logic, the set of operators "not" and "or" is described as orthogonal, but the set "nand", "or", and "not" is not (because any one of these can be expressed in terms of the others).
Also used loosely to mean "irrelevant to", e.g. "This may be orthogonal to the discussion, but ...", similar to "going off at a tangent".
[Jargon File]
(2002-12-02)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
The interplay between solid and void, transparency and opacity, curved and
orthogonal forms.
Teaching is pretty much orthogonal to using technology, even if you teach high
technology.
On this system, goodness and evil were represented as orthogonal to that
lawful-chaotic axis.
In the view above, the main subduction zone where the plate motions are more
orthogonal are further south.
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