Dual

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},
           {dual}, {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},
       {dual}, {twofold}, {two-fold}, {treble}, {threefold}, {three-
       fold}]
    3: 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"
    

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.
   [1913 Webster]

         Here you have one half of our dual truth. --Tyndall.
   [1913 Webster]
    

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.

   (1997-03-16)
    

43 Moby Thesaurus words for "dual":
      Janus-like, ambidextrous, bifacial, bifold, biform, bifurcated,
      bilateral, binary, binate, biparous, bipartisan, bipartite,
      bivalent, conduplicate, dichotomous, disomatous, double,
      double-barreled, double-faced, duadic, dualistic, duple, duplex,
      duplicate, duplicated, dyadic, geminate, geminated, identical,
      matched, paired, second, secondary, twain, twin, twinned, two,
      two-faced, two-level, two-ply, two-sided, two-story, twofold