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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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.


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