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# orthogonal

[ awr-**thog**-*uh*-nl ]

## adjective

*Mathematics.*- (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
- (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.
- (of two vectors) having an inner product equal to zero.
- (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
- (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.*

orthogonal

/ ɔːˈθɒɡənəl /

## adjective

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

orthogonal

/ ôr-thŏg**′**ə-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.

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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 orthogonal^{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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## Related Words

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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.

### Did you know ... ?

**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.

@GoodNotesApp big kudos for the new shape tool improvements. Been waiting for ages on this. While a whole lot better, maybe the degree of orthogonal filtering could be adjustable? this would be useful for drawing squares/rectangles

— Simon (@essweebee) March 24, 2020

There is the demographic in power, threatened with losing power, fighting to preserve it. There is an unwieldy coalition of outsider demographics, fighting to spread the power/money/privileges more broadly & fairly. The "size of gov't" debate is orthogonal to that, a sideshow.

— David Roberts (@drvox) April 14, 2020

That's the thing. My friends in history will tell you that the present makes enormous efforts to ignore, forget, lie, cheat, or otherwise condemn the past. The present has typically an orthogonal relationship with the past. Disease straightens the relationship.

— Stephen T Casper (@TheNeuroTimes) March 29, 2020

### 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.*

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