# 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.

## RELATED CONTENT

How Tetris Got Its NameFor over two decades, the puzzle video game Tetris has provided countless hours of procrastination and enjoyment for players all over the globe. But now, researchers believe that Tetris might have a new purpose. They think that the game may help to prevent the flashbacks that occur in the early stages of post-traumatic stress disorder. While the research is fascinating, let’s turn our attention to …

## Nearby words

- orthogenic,
- orthognathia,
- orthognathic,
- orthognathic surgery,
- orthognathous,
- orthogonal matrix,
- orthogonal projection,
- orthogonal trajectory,
- orthogonalize,
- orthograde

## Origin of orthogonal

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

## 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

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

## 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

## 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.