单词 | cauchy–schwarz |
释义 | Cauchy–Schwarzn. Mathematics. Cauchy–Schwarz inequality n. the statement that for any two sets of n numbers, the sum of the n pairwise sums, squared, is no greater than the sum of the two sums formed by adding the squared magnitudes of the numbers in each set. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > inequality inequation1855 inequality1875 Minkowski inequality1932 triangle inequality1941 Cauchy–Schwarz inequality1956 ultrametric inequality1967 1956 B. Friedman Princ. & Techniques Appl. Math i. 6 |〈x, y〉| ≦ |x| · |y|. This result is known as the Cauchy–Schwartz inequality. 1957 T. M. Apostol Math. Analysis i. 6 We shall now derive a very useful result known as the Cauchy–Schwarz inequality. 1988 Nature 24 Mar. 329/1 Another interesting relation among these quantities is obtained by applying the Cauchy–Schwarz inequality to equations (1) to (3). This entry has not yet been fully updated (first published 1997; most recently modified version published online June 2018). < n.1956 |
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