orthogonal

adjective

or·​thog·​o·​nal ȯr-ˈthä-gə-nᵊl 

1

a

: intersecting or lying at right angles

In orthogonal cutting, the cutting edge is perpendicular to the direction of tool travel.

b

: having perpendicular slopes or tangents at the point of intersection

orthogonal curves

2

: having a sum of products or an integral (see integral entry 1 sense 1b) that is zero or sometimes one under specified conditions: such as

a

of real-valued functions : having the integral of the product of each pair of functions over a specific interval equal to zero

b

of vectors : having the scalar product equal to zero

c

of a square matrix : having the sum of products of corresponding elements in any two rows or any two columns equal to one if the rows or columns are the same and equal to zero otherwise : having a transpose with which the product equals the identity matrix

3

of a linear transformation : having a matrix (see matrix sense 5a) that is orthogonal : preserving length and distance

4

: composed of mutually orthogonal elements

an orthogonal basis of a vector space

5

: statistically independent

mental ability may be classified into several orthogonal … factors

—O. D. Duncan

6

: orthographic sense 1

orthogonal projection

orthogonality

ȯr-ˌthä-gə-ˈna-lə-tē 

noun

orthogonally

ȯr-ˈthä-gə-nᵊl-ē 

adverb

Examples of orthogonal in a Sentence

Recent Examples on the Web

In a 10,000-dimensional space there are millions of nearly orthogonal vectors. —Anil Ananthaswamy, Quanta Magazine, 13 Apr. 2023

North African Jewish and non-Jewish populations form distinctive, orthogonal clusters. —Razib Khan, Discover Magazine, 13 Aug. 2012

In 10,000-dimensional space, there are 10,000 such mutually orthogonal vectors. —Anil Ananthaswamy, Quanta Magazine, 13 Apr. 2023

This duality is orthogonal at best. —Neil Senturia, San Diego Union-Tribune, 1 Nov. 2021

Next, ceramic spheres and compressed aluminum powder rods are stacked in an orthogonal, grillage pattern and enclosed in a steel box using spot welds. —Caroline Delbert, Popular Mechanics, 20 July 2020

The distance between the two towns can be measured on three (orthogonal) dimensions: longitude, latitude, and altitude. —Neuroskeptic, Discover Magazine, 9 Jan. 2012

This direction favors subsequent hydraulic fractures being orthogonal to the well. —Ian Palmer, Forbes, 19 May 2022

But anything that conducts an electric field also conducts a magnetic field in the orthogonal direction. —James Conca, Forbes, 27 Sep. 2021

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Word History

Etymology

Middle French, from Latin orthogonius, from Greek orthogōnios, from orth- + gōnia angle — more at -gon

First Known Use

circa 1560, in the meaning defined at sense 1a

Medical Definition

orthogonal

adjective

or·​thog·​o·​nal ȯr-ˈthäg-ən-ᵊl 

1

a

: lying or intersecting at right angles

b

: being, using, or made with three ECG leads whose axes are perpendicular to each other and to the frontal, horizontal, and sagittal axes of the body

the three orthogonal leads were recorded simultaneously on magnetic tape

—Massoud Nemati et al.

2

: statistically independent

mental ability may be classified into several orthogonal … factors

—O. D. Duncan