orthogonal

USAGE SUMMARY

The word 'orthogonal' is correct and usable in written English.
It is an adjective used to describe two lines, planes, or surfaces that intersect at right angles. Example sentence: The walls of the room were orthogonal, creating a perfect 90 degree corner.

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The fact that these three vectors corresponding to three possible results of measurement in one spatial direction are mutually orthogonal illustrates the different senses of orthogonality in H3 and in physical space.

SEP

By slightly weakening the assumption of orthogonality, and instead assuming that the various gi are only approximately orthogonal, we can avoid this difficulty, however.

SEP

In communications, the technique is known as orthogonal frequency division multiplexing, or OFDM.

The Economist

However, it seems to me that he addresses a set of issues orthogonal to those raised by Barack Obama's now infamous speech and discussed in my initial post about it.So why not look at the burden of all taxes?

The Economist

Such reconstruction is almost impossible with a single wide-band signal.The orthogonal part of OFDM is unique to wireless.

The Economist

Martin Rofheart, the co-founder of XtremeSpectrum and now the head of Freescale's UWB operation, says a faster chip, capable of 220 megabits per second, will be ready by the end of the year, with 480-megabit and 1-gigabit chips to follow in 2005.The rival approach, backed by the MBOA, is called multiband orthogonal frequency-division multiplexing (MB-OFDM).

The Economist

Flarion Technologies, a start-up firm backed by Cisco Systems, among others, has an approach based on OFDM (orthogonal frequency division multiplexing), the technology used in the fastest types of Wi-Fi and some digital-television systems.

The Economist

Dawkins classifies replicators using two orthogonal distinctions.

SEP

Far from conflicting with or even being orthogonal to the search for truth and our efforts to render our beliefs maximally responsive to the evidence, Quine insists, revising our beliefs in accordance with such pragmatic principles "at bottom, is what evidence is" (1955, 251).

SEP

Since the gate functions linearly, it must instead produce a state that is a linear superposition of the outputs obtained for the two orthogonal qubits.

SEP

This may not be an altogether misleading characterization of Paivio's actual view – he frequently refers to imagery as "modality specific" representation – but he clearly regards the distinction by sense mode between different types of image to be orthogonal to the more central distinction of Dual Coding Theory, between the image and the verbal (symbolic) codes.

SEP

Expert writing Tips

Best practice

When using "orthogonal" in technical contexts, ensure that the concept of independence or right angles is clearly implied and relevant to the discussion.

Common error

Avoid using "orthogonal" loosely when "independent" or "unrelated" would be more appropriate. "Orthogonal" carries a specific connotation of right angles or statistical independence that should be honored.

Linguistic Context

The word "orthogonal" functions primarily as an adjective. It describes the relationship between two entities that are at right angles or are statistically independent. Ludwig AI confirms that this word is used correctly and is usable in English.

Expression frequency: Very common

Frequent in

Science

73%

News & Media

26%

Formal & Business

1%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The word "orthogonal" is a grammatically correct adjective, predominantly used in formal and scientific contexts to describe elements that are independent or at right angles. According to Ludwig, "orthogonal" finds its primary use in Science and News & Media. To ensure accurate usage, consider the specific connotations of independence or right angles it implies, especially in technical discussions. While it can sometimes overlap with "independent", it's crucial to maintain awareness of its specific mathematical or statistical implications. Be aware of other terms with similar meanings: "perpendicular", "independent", and "unrelated".

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

perpendicular

Specifically refers to lines, planes, or surfaces meeting at a right angle, a more geometric interpretation.

independent

Implies a lack of influence or correlation between two or more things.

unrelated

Indicates that two or more things have no connection or association.

irrelevant

Suggests that something is not pertinent or applicable to the matter at hand.

tangential

Describes something that is slightly connected but not directly relevant.

distinct

Emphasizes the separate and clear nature of two or more things.

non-overlapping

Indicates that two or more things do not share any common elements or space.

mutually exclusive

Signifies that two or more things cannot occur or be true at the same time.

separate

Simply states that two or more things are not connected or combined.

unconnected

Implies a lack of any link or relationship between two or more things.

FAQs

How is "orthogonal" used in technical contexts?

In technical fields like mathematics, physics, and engineering, "orthogonal" describes vectors, functions, or signals that are at right angles or statistically independent, ensuring they do not interfere with each other.

What does it mean when two aspects are said to be "orthogonal"?

When two aspects of a problem are described as "orthogonal", it means they can be treated separately without affecting each other. The content of the message should be "independent of" the means of its delivery.

Can I use "orthogonal" interchangeably with "independent"?

While "orthogonal" and "independent" can sometimes overlap in meaning, they are not always interchangeable. "Orthogonal" often implies a more specific mathematical or statistical sense of independence, while "independent" is more general. Use "independent" if it's more intuitive.

What are some common examples of "orthogonal" concepts in mathematics?

Common examples include "perpendicular lines", which intersect at right angles, and vectors with a zero inner product. These concepts are used to ensure that elements do not interfere with each other in a given system.