A dual pair is a 3-tuple consisting of two vector spaces and over the same (real or complex) field and a bilinear form
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Some articles on dual pair:
... 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 ...
... In the mathematical field 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 is the centralizer of G′ in Sp(W ... 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 ...
... Associated with a dual pair is an injective linear map from to given by There is an analogous injective map from to ...
... 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 ...
Famous quotes containing the words pair and/or dual:
“Oh, Jacques, were used to each other, were a pair of captive hawks caught in the same cage, and so weve grown used to each other. Thats what passes for love at this dim, shadowy end of the Camino Real.”
—Tennessee Williams (19141983)
“Thee for my recitative,
Thee in the driving storm even as now, the snow, the winter-day
Thee in thy panoply, thy measurd dual throbbing and thy beat
Thy black cylindric body, golden brass and silvery steel,”
—Walt Whitman (18191892)