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dual    音标拼音: [d'uəl] [d'ul]
a. 双重的,双的
n. 双数

双重的,双的双数

dual
逻辑被动自动对偶 LPSD


dual
自对偶

dual
双

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" [synonym: {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 [synonym: {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]

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

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)


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