Historical Note
Hilbert (1894) introduced the Hilbert matrix to study the following question in approximation theory: "Assume that I = is a real interval. Is it then possible to find a non-zero polynomial P with integral coefficients, such that the integral
is smaller than any given bound ε > 0, taken arbitrarily small?" To answer this question, Hilbert derives an exact formula for the determinant of the Hilbert matrices and investigates their asymptotics. He concludes that the answer to his question is positive if the length b − a of the interval is smaller than 4.
Read more about this topic: Hilbert Matrix
Famous quotes containing the words historical and/or note:
“This seems a long while ago, and yet it happened since Milton wrote his Paradise Lost. But its antiquity is not the less great for that, for we do not regulate our historical time by the English standard, nor did the English by the Roman, nor the Roman by the Greek.... From this September afternoon, and from between these now cultivated shores, those times seemed more remote than the dark ages.”
—Henry David Thoreau (1817–1862)
“His ear is so sensitively attuned to the bugle note of history that he is often deaf to the more raucous clamour of contemporary life.”
—Aneurin Bevan (1897–1960)