# orthogonal

### adjective

- Also orthographic. pertaining to or involving right angles or perpendiculars: an orthogonal projection.
- (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.

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## Origin of orthogonal

## OTHER WORDS FROM orthogonal

or·thog·o·nal·i·ty, nounor·thog·o·nal·ly, adverb## Words nearby orthogonal

## VOCAB BUILDER

### 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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## British Dictionary definitions for orthogonal

### adjective

- (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