Cauchy–Schwarzn.

/kəʊʃɪˈʃvɑːts/

Etymology: < the names of Augustin-Louis Cauchy (see Cauchy n.) and Hermann Amadeus Schwarz (see Schwarz n.).

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).

单词	cauchy–schwarz
释义	Cauchy–Schwarzn. /kəʊʃɪˈʃvɑːts/ Etymology: < the names of Augustin-Louis Cauchy (see Cauchy n.) and Hermann Amadeus Schwarz (see Schwarz n.). 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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