dual

(redirected from dualising)
Also found in: Dictionary, Thesaurus, Legal.

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 ?
For each definition expressed in the categorical language, of a concept or construction xxx, you obtain another concept, often called co-xxx if no better name suggests itself, by dualising each term in the definition (Fokkinga (20)).
The first one is to provide consultancy services for the design and supervision of dualising Raysut-Al Mughsayl road in Dhofar, while the second one is to provide consultancy services for design and built extension of Tanam-Ramlat Khaila road in Ibri.
Also included are additional works on dualisation of the road from Al Zarob R/A-Al Buarimi Hospital R/A (RO 1,813,691); works on dualising 23 July Road in Salalah (RO1,668,788); additional works on security guard services for 200 sites of Public Authority for Electricity and Water (RO 1,411,410).