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# orthogonal

[awr-thog-uh-nl] /ɔrˈθɒg ə nl/
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 of orthogonal
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
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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British Dictionary definitions for orthogonality

## orthogonal

/ɔːˈθɒɡənəl/
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
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for orthogonality

## orthogonal

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)    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.
The American Heritage® Science Dictionary
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### Difficulty index for orthogonal

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### Word Value for orthogonality

0
21
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