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)
“Firm-style bean curd insoles cushion feet, absorb perspiration and provide more protein than meat or fish innersoles of twice the weight. Tofu compresses with use, becoming more pungent and flavorful. May be removed when not in use to dry or marinate. Innersoles are ready to eat after 1,200 miles of wear. Each pair provides adult protein requirement for 2 meals. Insoles are sized large to allow for snacks. Recipe booklet included.”
—Alfred Gingold, U.S. humorist. Items From Our Catalogue, “Tofu Innersoles,” Avon Books (1982)