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.

Read more about Dual Pair:  Example, Comment

Famous quotes containing the words dual and/or pair:

    “Thee for my recitative,
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    declining,
    Thee in thy panoply, thy measur’d dual throbbing and thy beat
    convulsive,
    Thy black cylindric body, golden brass and silvery steel,”
    —Walt Whitman (1819–1892)

    “You are always looking for already-felt emotions, just as you like to get an old pair of trousers back from the cleaners, which seem new when you don’t look too closely. Artists are cleaners, don’t let yourself be taken in by them. True modern works of art are made not by artists but quite simply by men.”
    —Francis Picabia (1878–1953)