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)
“With two sons born eighteen months apart, I operated mainly on automatic pilot through the ceaseless activity of their early childhood. I remember opening the refrigerator late one night and finding a roll of aluminum foil next to a pair of small red tennies. Certain that I was responsible for the refrigerated shoes, I quickly closed the door and ran upstairs to make sure I had put the babies in their cribs instead of the linen closet.”
—Mary Kay Blakely (20th century)