# dual

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## dual

Maths Logic (of structures or expressions) having the property that the interchange of certain pairs of terms, and usually the distribution of negation, yields equivalent structures or expressions

## dual

i. Duplicated controls permitting either an instructor and a pupil or the pilot and the copilot to operate controls.
ii. Instructional flying hours or sorties logged in a flying log by the pupil.

## dual

(mathematics)
Every field of mathematics has a different meaning of dual. Loosely, where there is some binary symmetry of a theory, the image of what you look at normally under this symmetry is referred to as the dual of your normal things.

In linear algebra for example, for any vector space V, over a field, F, the vector space of linear maps from V to F is known as the dual of V. It can be shown that if V is finite-dimensional, V and its dual are isomorphic (though no isomorphism between them is any more natural than any other).

There is a natural embedding of any vector space in the dual of its dual:

V -> V'': v -> (V': w -> wv : F)

(x' is normally written as x with a horizontal bar above it). I.e. v'' is the linear map, from V' to F, which maps any w to the scalar obtained by applying w to v. In short, this double-dual mapping simply exchanges the roles of function and argument.

It is conventional, when talking about vectors in V, to refer to the members of V' as covectors.
References in periodicals archive ?
The proposed procedure for the inverse problem (dualising the original morphisms) is not very complicated, but may be difficult while looking for numerical implementations.
A total of RO240 million has been allocated by the government for dualising Bid Bid-Sur road.
Summary: Muscat: The Ministry of Transport and Communications yesterday floated two major tenders for dualising a ...
Muscat: The Ministry of Transport and Communications yesterday floated a major tender for dualising a section of the Bidbid-Sur road.
MUSCAT: Galfar Engineering and Contracting Company yesterday won a major contract for dualising the Izz-Adam section of the Nizwa-Thumrait road.

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