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:
“In public buildings set aside for the care and maintenance of the goods of the middle ages, a staff of civil service art attendants praise all the dead, irrelevant scribblings and scrawlings that, at best, have only historical interest for idiots and layabouts.”
—George Grosz (18931959)
“I note that the Africa loves to depict the grace of reptiles.”
—Zora Neale Hurston (18911960)