| 释义 |
Schwarz Math.|ʃvɑːts|
Also (erron.) Schwartz.
The name of Hermann Amadeus Schwarz (1843–1921), German mathematician, used attrib. 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.
1955M. Loève Probability Theory ix. 156 Hölder's inequality with r = s = 2, is called the Schwarz inequality: E2 {vb} XY {vb} {slle} E {vb} X {vb} 2.E {vb} Y {vb}2. 1962W. B. Thompson Introd. Plasma Physics viii. 222 This makes use of the Schwartz inequality ∫f2dx∫g2dx ⩾ [∫fgdx]2. 1964McCord & 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 {slle} [E(X1 - a)2][E(X2 - b)2], which is a form of Schwarz's inequality. 1965Patterson & Rutherford Elem. Abstr. Algebra v. 176 In a unitary space ‖ a‖ ‖ b‖ ⩾ {vb}a·b{vb}... The inequality is known as Schwartz's inequality. 1975Karlin & Taylor First Course Stochastic Processes (ed. 2) ix. 452, E[{vb}YZ{vb}] {slle} √(E[Y2]E[Z2]) = ‖ Y‖ ‖ Z‖ . This is known as Schwartz' inequality. |