A Topical Dictionary: Search for dual

Dictionary Results For "dual" [?]/[OPML]

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GNU Project's publication of CIDE, the Collaborative International Dictionary of English 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]

WordNet 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 two
items (plural); "ancient Greek had the dual form but it
has merged with the plural form in modern Greek"

Moby Dictionary
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

FOLDOC 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.

(1997-03-16)