# 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

## Related Words for orthogonal

rectangular, quadrate, quadratic, equilateral, foursquare, boxlike, boxy, orthogonal, rectilinear, squarish## Examples from the Web for orthogonal

### Contemporary Examples of orthogonal

### Historical Examples of orthogonal

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.