# orthogonal

[ awr-thog-uh-nl ]
/ ɔrˈθɒg ə nl /
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Mathematics.
1. Also orthographic. pertaining to or involving right angles or perpendiculars: an orthogonal projection.
2. (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
3. (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.
4. (of two vectors) having an inner product equal to zero.
5. (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
6. (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.
having no bearing on the matter at hand; independent of or irrelevant to another thing or each other: It’s an interesting question, but orthogonal to our exploration of the right to privacy.
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## Origin oforthogonal

First recorded in 1565–75; obsolete orthogon(ium) “right triangle,” from Late Latin orthogōnium or directly from Greek orthogṓnion (neuter) “right-angled,” equivalent to ortho-ortho- + -gōnion-gon) + -al1

## OTHER WORDS FROM orthogonal

or·thog·o·nal·i·ty [awr-thog-uh-nal-i-tee], /ɔrˌθɒg əˈnæl ɪ ti/, nounor·thog·o·nal·ly, adverb

## Words nearby orthogonal

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

## What does orthogonal mean?

Orthogonal means relating to or involving lines that are perpendicular or that form right angles, as in This design incorporates many orthogonal elements. Another word for this is orthographic.

When lines are perpendicular, they intersect or meet to form a right angle. For example, the corners of squares and rectangles are all right angles.

Orthogonal is a mathematical term that is also used in much more technical ways pertaining to vectors and functions.

However, orthogonal is also sometimes used in a figurative way meaning unrelated, separate, in opposition, or irrelevant. In this sense, it means about the opposite of parallel when parallel means corresponding or similar.

Example: Not everything happens according to a grand scheme—some events are simply orthogonal to each other.

## Where does orthogonal come from?

The first records of orthogonal in English come from the 1500s. It ultimately comes from the Greek orthogṓnion, meaning “right-angled (shape).” This Greek root is composed of the elements ortho-, “straight, upright, right,” and –gōnion, “angled.”

Orthogonal is commonly used in mathematics, geometry, statistics, and software engineering. Most generally, it’s used to describe things that have rectangular or right-angled elements. More technically, in the context of vectors and functions, orthogonal means “having a product equal to zero.”

More recently, orthogonal has come to be used in a figurative way. It’s typically applied to two things to describe them as independent of or irrelevant to each other. Sometimes it implies that they are in opposition to each other in some way, perhaps because they have divergent goals or outcomes or causes.

## Did you know ... ?

What are some other forms related to orthogonal?

• orthogonality (noun)

What are some synonyms for orthogonal?

What are some words that share a root or word element with orthogonal

What are some words that often get used in discussing orthogonal?

## How is orthogonal used in real life?

Orthogonal is commonly used in the context of things designed with right angles. It’s figurative use is often applied to events considered unrelated to each other.

## Try using orthogonal!

Is orthogonal used correctly in the following sentence?

The bridge’s orthogonal design not only makes it aesthetically pleasing but also structurally sound.

## British Dictionary definitions for orthogonal

orthogonal
/ (ɔːˈθɒɡənəl) /

relating to, consisting of, or involving right angles; perpendicular
maths
1. (of a pair of vectors) having a defined scalar product equal to zero
2. (of a pair of functions) having a defined product equal to zero
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