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:
“The proverbial notion of historical distance consists in our having lost ninety-five of every hundred original facts, so the remaining ones can be arranged however one likes.”
—Robert Musil (1880–1942)
“During the cattle drives, Texas cowboy music came into national significance. Its practical purpose is well known—it was used primarily to keep the herds quiet at night, for often a ballad sung loudly and continuously enough might prevent a stampede. However, the cowboy also sang because he liked to sing.... In this music of the range and trail is “the grayness of the prairies, the mournful minor note of a Texas norther, and a rhythm that fits the gait of the cowboy’s pony.””
—Administration in the State of Texa, U.S. public relief program (1935-1943)