Schwarzn.
/ʃvɑːts/ Mathematics.
Used attributively and in the possessive to designate the various forms of the theorem which states that the square of the sum of a set of products of two quantities cannot exceed the sum of the squares of the first terms multiplied by the sum of the squares of the second terms. Chiefly in Schwarz inequality.
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the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem
pons asinorum1718
Fermat's theorem1845
Bernoulli's theorem1865
Fermat's last theorem1865
Fourier's theorem1880
remainder theorem1886
Stokes' theorem1893
Jordan('s) (curve) theorem1900
Waring's theorem1920
Gödel's theorem1933
maximin1953
incompleteness theorem1955
Schwarz inequality1955
1955 M. Loève Probability Theory ix. 156 Hölder's inequality with r = s = 2, is called the Schwarz inequality: E2 | XY | ≤ E | X | 2.E | Y |2.
1962 W. B. Thompson Introd. Plasma Physics viii. 222 This makes use of the Schwartz inequality ∫f2dx∫g2dx ≥ [∫fgdx]2.
1964 McCord & Moroney Introd. Probability Theory ix. 155 Let X1 and X2 be any two jointly distributed random variables which have finite, positive variances... If a and b are any real constants deduce that [E(X1 − a)(X2 − b)]2 ≤ [E(X1 − a)2][E(X2 − b)2], which is a form of Schwarz's inequality.
1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra v. 176 In a unitary space ‖a‖ ‖b‖ ≥ |a·b|... The inequality is known as Schwartz's inequality.
1975 Karlin & Taylor First Course Stochastic Processes (ed. 2) ix. 452 E[|YZ|] ≤ √(E[Y2]E[Z2]) = ‖Y‖ ‖Z‖. This is known as Schwartz' inequality.
This entry has not yet been fully updated (first published 1982; most recently modified version published online June 2022).
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n.1955