A dual pair is a 3-tuple consisting of two vector spaces and over the same (real or complex) field and a bilinear form
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":
... Associated with a dual pair is an injective linear map from to given by There is an analogous injective map from to ...
... 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 ...
... 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 ...
... 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 GunsnRoses lyric attended by every ofay insurance broker in America who owns a pair of white shoes.”
—P.J. (Patrick Jake)
“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)