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

More orthogonal in spirit, the sister’s side features a central staircase and internal windows so that the primary suite overlooks the kitchen and dining area, borrowing light from the rear façade. —Sam Cochran, Architectural Digest, 18 Mar. 2025

Nick Bostrom, in Superintelligence, presents Hume’s position as an orthogonality thesis: Intelligence and final goals are orthogonal: more or less any level of intelligence could in principle be combined with more or less any final goal. —IEEE Spectrum, 8 Oct. 2019

Disks with orthogonal cuts 1.5 millimeters long and 250 microns wide could reach 4 millimeters when exposed to the magnetic field, more than twice as high as domes without them. —Ars Technica, 27 Dec. 2024

Goeritz, a towering figure in Mexican modern art and architecture, challenged the young architect’s initial design of rigid orthogonal spaces. —Natalie Stoclet, Forbes, 5 Dec. 2024

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