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.
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)
“... the Ovarian Theory of Literature, or, rather, its complement, the Testicular Theory. A recent camp follower ... of this explicit theory is ... Norman Mailer, who has attributed his own gift, and the literary gift in general, solely and directly to the possession of a specific pair of organs. One writes with these organs, Mailer has said ... and I have always wondered with what shade of ink he manages to do it.”
—Cynthia Ozick (b. 1928)