orthogonality

orthogonal

[awr-thog-uh-nl]
adjective
1.
Mathematics.
a.
Also, orthographic. 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
orthogonally, adverb
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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 
  1. Relating to or composed of right angles.

  2. Relating to a matrix whose transpose equals its inverse.

  3. Relating to a linear transformation that preserves the length of vectors.


The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Slang Dictionary

orthogonal

adj. [from mathematics] Mutually independent; well separated; sometimes, irrelevant to. Used in a generalization of its mathematical meaning to describe sets of primitives or capabilities that, like a vector basis in geometry, span the entire `capability space' of the system and are in some sense non-overlapping or mutually independent. For example, in architectures such as the PDP-11 or VAX where all or nearly all registers can be used interchangeably in any role with respect to any instruction, the register set is said to be orthogonal. Or, in logic, the set of operators `not' and `or' is 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 in comments on human discourse: "This may be orthogonal to the discussion, but...."
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