# orthogonally

## 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
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Based on the Random House Dictionary, © Random House, Inc. 2013.
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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.
The American Heritage® Science Dictionary