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)
“There are two kinds of truth; the truth that lights the way and the truth that warms the heart. The first of these is science, and the second is art.... Without art science would be as useless as a pair of high forceps in the hands of a plumber. Without science art would become a crude mess of folklore and emotional quackery.”
—Raymond Chandler (1888–1959)