[ awr-thog-uh-nl ]
/ ɔrˈθɒg ə nl /
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  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.



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Origin of orthogonal

1565–75; obsolete orthogon(ium) right triangle (<Late Latin orthogōnium<Greek orthogṓnion (neuter) right-angled, equivalent to ortho-ortho- + -gōnion-gon) + -al1
or·thog·o·nal·i·ty, nounor·thog·o·nal·ly, adverb
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2021


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.

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What are some other forms related to orthogonal?

  • orthogonality (noun)
  • orthogonally (adverb)

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

/ (ɔːˈθɒɡənəl) /


relating to, consisting of, or involving right angles; perpendicular
  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
orthogonally, adverb
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

Scientific definitions for orthogonal

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