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,
    Thee in the driving storm even as now, the snow, the winter-day
    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)

    “I well recall my horror when I heard for the first time, of a journalist who had laid in a pair of what were then called bicycle pants and taken to golf; it was as if I had encountered a studhorse with his hair done up in frizzes, and pink bowknots peeking out of them. It seemed, in some vague way, ignominious, and even a bit indelicate.”
    —H.L. (Henry Lewis)