# orthogonal

[ awr-thog-uh-nl ]
See synonyms for orthogonal on Thesaurus.com
adjective
1. 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.

2. Crystallography. referable to a rectangular set of axes.

1. 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.

## Origin of orthogonal

1
First recorded in 1565–75; obsolete orthogon(ium) “right triangle,” from Late Latin orthogōnium or directly from Greek orthogṓnion (neuter) “right-angled,” equivalent to ortho-ortho- + -gōnion-gon) + -al1

## Other words from orthogonal

• or·thog·o·nal·i·ty [awr-thog-uh-nal-i-tee], /ɔrˌθɒg əˈnæl ɪ ti/, noun
• or·thog·o·nal·ly, adverb

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024

## 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
1. relating to, consisting of, or involving right angles; perpendicular

2. 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, 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

## Scientific definitions for orthogonal

orthogonal

[ ôr-thŏgə-nəl ]

1. Relating to or composed of right angles.

2. Relating to a matrix whose transpose equals its inverse.

1. 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.