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:
“Reason, progress, unselfishness, a wide historical perspective, expansiveness, generosity, enlightened self-interest. I had heard it all my life, and it filled me with despair.”
—Katherine Tait (b. 1923)
“Is whispering nothing?
Is leaning cheek to cheek? Is meeting noses?
Kissing with inside lip? Stopping the career
Of laughter with a sigh?—a note infallible
Of breaking honesty.”
—William Shakespeare (1564–1616)