a dual of

USAGE SUMMARY

The phrase "a dual of" is correct and usable in written English.
It is typically used in mathematical or theoretical contexts to refer to a dual relationship between structures or concepts. Example: "In linear algebra, the dual of a vector space consists of all linear functionals defined on that space."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

15 human-written examples

Our first result is a dual of Theorem 4.1.

Bulletin of Mathematical Sciences

The hitting set problem is a "dual" of the set cover problem.

EURASIP Journal on Wireless Communications and Networking

Shibuya, K. Sakaniwa, A dual of well-behaving type designed minimum distance, IEICE Trans.

Finite Fields and Their Applications

Moreover, it is shown that both spaces are BK-spaces, and one is a dual of another.

Journal of Inequalities and Applications

Note that HS is a dual of SC, and hence solving HS is sufficient to solve SC.

EURASIP Journal on Wireless Communications and Networking

end{aligned} (3 On the other hand, the necessity measure of an event (tilde{a}star tilde{b}) is a dual of the possibility measure.

Vietnam Journal of Computer Science

Human-verified similar examples from authoritative sources

Similar Expressions

44 human-written examples

It consists of a dual process of intelligence gathering and target extraction.

Huffington Post

In 1964, the court found in favor of the students and ruled that the district was "violating the Constitution by its operation of a dual system of education".

Huffington Post

B'Tselem has also documented Israel's application of a "dual system of law" that grants settlers significant leniency, thereby allowing them to continue their attacks.

Huffington Post

We have observed evidence of a dual function of ITAM-adapter signaling in osteoclasts.

Plosone

The cardiovascular effects of a dual blockage of RAS require mention.

Diabetes Care

Expert writing Tips

Best practice

In technical writing, define the precise meaning of 'dual' in your specific field to avoid ambiguity.

Common error

Avoid using "a dual of" loosely to simply mean 'opposite' without the specific mathematical or logical relationship implied by the term. Use "the opposite of" when you indicate a direct contrast.

Linguistic Context

The phrase "a dual of" functions as a relational term, indicating that one concept or entity is the dual of another. It is often used to establish a specific mathematical or logical relationship between two elements. As indicated by Ludwig, the phrase is grammatically correct and usable.

Expression frequency: Common

Frequent in

Science

70%

News & Media

20%

Encyclopedias

10%

Less common in

Formal & Business

0%

Wiki

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, the phrase "a dual of" is a relational term primarily used in academic and scientific contexts to define a specific relationship between two entities. Ludwig AI confirms its grammatical correctness. While alternatives like "the counterpart of" exist, using "a dual of" implies a particular mathematical or logical connection. Therefore, it is crucial to ensure the context aligns with the technical meaning of duality. The phrase is common and appears in journals and publications like EURASIP Journal on Wireless Communications and Networking and Vietnam Journal of Computer Science.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the counterpart of

This phrase suggests a corresponding element or concept, implying a similar but distinct entity.

the inverse of

This phrase indicates an opposite or reverse relationship, often used in mathematical or logical contexts.

the complement of

This refers to something that completes or balances another, often in a set-theoretic or logical sense.

the converse of

Similar to inverse, this emphasizes a reversed relationship, particularly in logic or mathematics.

the opposite of

Indicates a direct contrast or antithesis between two things.

the mirror image of

Suggests a reflected or symmetrical relationship, implying similarity in form but difference in orientation.

the flip side of

Indicates another aspect or perspective of the same thing, often with contrasting characteristics.

the other side of the coin

Similar to "the flip side of", this highlights a contrasting aspect of the same situation or concept.

the analogue of

Implies a similarity or correspondence in function or structure, often used in scientific or technical contexts.

the reciprocal of

This phrase is generally used in mathematics to indicate a number that, when multiplied by the original number, equals 1.

FAQs

How is "a dual of" used in mathematics?

In mathematics, "a dual of" often refers to a structure derived from another structure, such as the dual space of a vector space, which consists of all linear functionals on that space. It indicates a specific mathematical relationship.

What is an alternative to "a dual of" that doesn't imply a formal relationship?

If you want to express a general contrasting relationship without the technical implications, consider using phrases like "the opposite of" or "the counterpart of".

In what contexts is "a dual of" most appropriate?

"A dual of" is most appropriate in academic, scientific, and technical contexts where duality has a specific, well-defined meaning. Using it outside these areas can be misleading.

How does "a dual of" differ from "the inverse of"?

While both suggest a reversed or opposite relationship, "a dual of" usually implies a more complex and specific connection between two structures, whereas "the inverse of" often refers to a direct reversal or negation, especially in mathematics.