- 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.
Origin of orthogonal
OTHER WORDS FROM orthogonalor·thog·o·nal·i·ty [awr-thog-uh-nal-i-tee], /ɔrˌθɒg əˈnæl ɪ ti/, nounor·thog·o·nal·ly, adverb
Words nearby orthogonal
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?
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.
How to use orthogonal in a sentence
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.Lasers reveal construction inspired by ancient Mexican pyramids in Maya ruins|Meghie Rodrigues|October 22, 2021|Science News
This use of orthogonal coding to separate and protect information in the brain has been seen before.The Brain ‘Rotates’ Memories to Save Them From New Sensations|Jordana Cepelewicz|April 15, 2021|Quanta Magazine
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 Brain ‘Rotates’ Memories to Save Them From New Sensations|Jordana Cepelewicz|April 15, 2021|Quanta Magazine
The two orthogonal representations can then draw from overlapping neural activity without intruding on each other.The Brain ‘Rotates’ Memories to Save Them From New Sensations|Jordana Cepelewicz|April 15, 2021|Quanta Magazine
Actually, the issue of plural vs. singular is orthogonal to the dilemma she wants to pose.Responding To Critics Of "On Questioning The Jewish State"|Joseph Levine|March 18, 2013|DAILY BEAST
They also seem to be a bit orthogonal to the kinds of structures that medicinal chemists make.Worried About Incurable Tuberculosis? Stand By for Incurable Everything.|Megan McArdle|March 12, 2013|DAILY BEAST
And that brings up another question about those bacterial targets, the ones that are so orthogonal to human cellular pathways.Worried About Incurable Tuberculosis? Stand By for Incurable Everything.|Megan McArdle|March 12, 2013|DAILY BEAST
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.Kinematics of Mechanisms from the Time of Watt|Eugene S. Ferguson
British Dictionary definitions for orthogonal
- (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