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orthogonal

[awr-thog-uh-nl] /ɔrˈθɒg ə nl/
adjective
1.
Mathematics.
  1. Also, orthographic. pertaining to or involving right angles or perpendiculars:
    an orthogonal projection.
  2. (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
  3. (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.
  4. (of two vectors) having an inner product equal to zero.
  5. (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
  6. (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
1565-1575
1565-75; obsolete orthogon(ium) right triangle (< Late Latin orthogōnium < Greek orthogṓnion (neuter) right-angled, equivalent to ortho- ortho- + -gōnion -gon) + -al1
Related forms
orthogonality, noun
orthogonally, adverb
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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British Dictionary definitions for orthogonality

orthogonal

/ɔːˈθɒɡənəl/
adjective
1.
relating to, consisting of, or involving right angles; perpendicular
2.
(maths)
  1. (of a pair of vectors) having a defined scalar product equal to zero
  2. (of a pair of functions) having a defined product equal to zero
Derived Forms
orthogonally, adverb
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin and History for orthogonality

orthogonal

adj.

1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios "right-angled," from ortho- "straight" (see ortho-) + gonia "angle," related to gony "knee" (see knee (n.)). Related: Orthogonally.

Online Etymology Dictionary, © 2010 Douglas Harper
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orthogonality in Science
orthogonal
  (ôr-thŏg'ə-nəl)   
  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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