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De - Pt| English Dictionary: 'Dual | by the DICT Development Group |
| 2 results for 'Dual | |
| From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
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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 The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
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dual 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) | |
