| a. | 1. | Expressing, or consisting of, the number two; belonging to two; |
| Adj. | 1. | dual - consisting of or involving two parts or components usually in pairs; "an egg with a double yolk"; "a double (binary) star"; "double doors"; "dual controls for pilot and copilot"; "duple (or double) time consists of two (or a multiple of two) beats to a measure" |
| 2. | dual - having more than one decidedly dissimilar aspects or qualities; "a double (or dual) role for an actor"; "the office of a clergyman is twofold; public preaching and private influence"- R.W.Emerson; "every episode has its double and treble meaning"-Frederick Harrison | |
| 3. | dual - a grammatical number category referring to two items or units as opposed to one item (singular) or more than two items (plural); "ancient Greek had the dual form but it has merged with the plural form in modern Greek" |
| (mathematics) | dual - 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. |