# orthogonal

[awr-thog-uh-nl]

- 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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## Origin of orthogonal^{}

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## Examples from the Web for orthogonal

### Contemporary Examples

### Historical Examples

#### Velocities in linkages were determined by orthogonal components transferred from link to link.

Kinematics of Mechanisms from the Time of WattEugene S. Ferguson

#### In the first place, each of these figures may be conceived as an orthogonal projection of a closed plane-faced polyhedron.

#### The involutes are “orthogonal trajectories” of the tangents to the common evolute.

## orthogonal

- 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

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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

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.

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The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.