View synonyms for orthogonal


[ awr-thog-uh-nl ]


  1. Mathematics.
    1. Also 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.
  2. Crystallography. referable to a rectangular set of axes.
  3. 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.


/ ɔːˈθɒɡənəl /


  1. relating to, consisting of, or involving right angles; perpendicular
  2. 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


/ ôr-thŏgə-nəl /

  1. Relating to or composed of right angles.
  2. Relating to a matrix whose transpose equals its inverse.
  3. Relating to a linear transformation that preserves the length of vectors.

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Derived Forms

  • orˈthogonally, adverb

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Other Words From

  • or·thog·o·nal·i·ty [awr-thog-, uh, -, nal, -i-tee], noun
  • or·thog·o·nal·ly adverb

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Word History and Origins

Origin of orthogonal1

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 ) + -al 1

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Example Sentences

The very orthogonal city planning with specific orientation of the pyramids gives Teotihuacan a very characteristic architectural style, making it easy to identify any Teotihuacan influence abroad.

This use of orthogonal coding to separate and protect information in the brain has been seen before.

The memory representations were organized in what neuroscientists describe as an “orthogonal” dimension to the sensory representations, all within the same population of neurons.

The two orthogonal representations can then draw from overlapping neural activity without intruding on each other.

Actually, the issue of plural vs. singular is orthogonal to the dilemma she wants to pose.

They also seem to be a bit orthogonal to the kinds of structures that medicinal chemists make.

And that brings up another question about those bacterial targets, the ones that are so orthogonal to human cellular pathways.

The involutes are “orthogonal trajectories” of the tangents to the common evolute.

In the first place, each of these figures may be conceived as an orthogonal projection of a closed plane-faced polyhedron.

Velocities in linkages were determined by orthogonal components transferred from link to link.


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More About Orthogonal

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?

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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.



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Is orthogonal used correctly in the following sentence? 

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