# orthogonal

[ awr-thog-uh-nl ]

/ ɔrˈθɒg ə nl /

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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.

having no bearing on the matter at hand; independent of or irrelevant to another thing or each other: It’s an interesting question, but orthogonal to our exploration of the right to privacy.

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## Origin of orthogonal

## OTHER WORDS FROM orthogonal

or·thog·o·nal·i·ty [awr-thog-uh-nal-i-tee], /ɔrˌθɒg əˈnæl ɪ ti/, nounor·thog·o·nal·ly, adverbDictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2022

## How to use orthogonal in a sentence

Straight: Circle cutting the fundamental plane orthogonally.

Projecting orthogonally on a plane perpendicular to the central axis we obtain two reciprocal figures.

## 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 forms of orthogonal

orthogonally, adverbCollins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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## Scientific 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.