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 works of women are symbolical.
We sew, sew, prick our fingers, dull our sight,
Producing what? A pair of slippers, sir,
To put on when you’re weary or a stool
To stumble over and vex you ... “curse that stool!”
Or else at best, a cushion, where you lean
And sleep, and dream of something we are not,
But would be for your sake. Alas, alas!
This hurts most, this ... that, after all, we are paid
The worth of our work, perhaps.”
—Elizabeth Barrett Browning (1806–1861)