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more about dual
## dual |

3 definitions found From Webster's Revised Unabridged Dictionary (1913) [web1913]: Dual \Du"al\, a. [L. dualis, fr duo two See {Two}.] Expressing, or consisting of the number two belonging to two as the dual number of nouns, etc., in Greek. Here you have one half of our dual truth. --Tyndall. From WordNet r 1.6 [wn]: dual adj 1: 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" [syn: {double}, {duple}] 2: 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 [syn: {double}, {twofold}, {treble}, {threefold}] 3: a grammatical number category referring to two items or units (as opposed to one item (singular) or more than one item (plural)); "ancient Greek had the dual form but it has merged with the plural form in modern Greek" From The Free On-line Dictionary of Computing (13 Mar 01) [foldoc]: dualEvery 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 (1997-03-16)

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