# orthogonal

[ awr-thog-uh-nl ]

/ ɔrˈθɒg ə nl /

### adjective

Mathematics.

- Also orthographic. pertaining to or involving right angles or perpendiculars: an orthogonal projection.
- (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
- (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.
- (of two vectors) having an inner product equal to zero.
- (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
- (of a square matrix) defined so that its product with its transpose results in the identity matrix.

Crystallography. referable to a rectangular set of axes.

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## Nearby words

## Origin of orthogonal

Related formsor·thog·o·nal·i·ty, nounor·thog·o·nal·ly, adverb

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

## Examples from the Web for orthogonal

## British Dictionary definitions for orthogonal

## orthogonal

/ (ɔːˈθɒɡənəl) /

### adjective

relating to, consisting of, or involving right angles; perpendicular

maths

- (of a pair of vectors) having a defined scalar product equal to zero
- (of a pair of functions) having a defined product equal to zero

Derived Formsorthogonally, adverb

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Word Origin and History for orthogonal

## 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

## Science definitions for orthogonal

## 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
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.