# Dual Pair

A dual pair is a 3-tuple consisting of two vector spaces and over the same (real or complex) field and a bilinear form

with

and

We say puts and in duality.

We call two elements and orthogonal if

We call two sets and orthogonal if any two elements of and are orthogonal.

### Other articles related to "dual pair, dual, pair, pairs":

Dual Pair - Comment
... Associated with a dual pair is an injective linear map from to given by There is an analogous injective map from to ...
Dou Di Zhu - Illegal Play With The Kicker
... Dual Solo = Pair Four /w Dual Solo 3-3-3-3 /w J-J Dual Solo must consist of two cards with different ranks, such as J-K ... Otherwise, it is counted as pair which is different ... Dual Pair = 4 Cards of the Same Rank Four /w Dual Pair 3-3-3-3 /w J-J-J-J Dual Pair must consist of two sets of pairs of different ranks, such as 3-3-7-7 ...
Quasiregular Polyhedron - The Convex Quasiregular Polyhedra
... Each of these forms the common core of a dual pair of regular polyhedra ... The names of two of these give clues to the associated dual pair, respectively the cube + octahedron and the icosahedron + dodecahedron ... The octahedron is the core of a dual pair of tetrahedra (an arrangement known as the stella octangula), and when derived in this way is sometimes called the tetratetrahedron ...
Reductive Dual Pair
... of representation theory, a reductive dual pair is a pair of subgroups (G, G′) of the isometry group Sp(W) of a symplectic vector space W, such that G ... Somewhat more loosely, one speaks of a dual pair whenever two groups are the mutual centralizers in a larger group, which is frequently a general linear group ...

### Famous quotes containing the words pair and/or dual:

The Republican convention, an event with the intellectual content of a Guns’n’Roses lyric attended by every ofay insurance broker in America who owns a pair of white shoes.
—P.J. (Patrick Jake)

Thee for my recitative,
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Thee in thy panoply, thy measur’d dual throbbing and thy beat
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Walt Whitman (1819–1892)