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searching for Cauchy–Schwarz inequality 8 found (138 total)

alternate case: cauchy–Schwarz inequality

Brezis–Gallouët inequality (1,004 words) [view diff] exact match in snippet view article find links to article

\end{aligned}}} owing to the preceding inequalities and to the Cauchy-Schwarz inequality. This yields ‖ v ^ ‖ L 1 ( R 2 ) ≤ C ( log ⁡ ( 1 + R ) ) 1 2 +

Borel–Cantelli lemma (2,329 words) [view diff] case mismatch in snippet view article find links to article

_{i=m}^{n}A_{i}\right)=\Pr(S_{m,n}>0).} Now, notice that by the Cauchy-Schwarz Inequality, E [ X ] 2 ≤ E [ X 1 { X > 0 } ] 2 ≤ E [ X 2 ] Pr ( X > 0 ) ,

Stress majorization (1,171 words) [view diff] exact match in snippet view article find links to article

_{j=1,j\neq i}^{n}b_{ij}} . Proof of this inequality is by the Cauchy-Schwarz inequality, see Borg (pp. 152–153). Thus, we have a simple quadratic function

Gelfand–Naimark–Segal construction (2,463 words) [view diff] exact match in snippet view article find links to article

:=\rho (b^{*}a),\;a,b\in A} , which is well-defined due to the Cauchy–Schwarz inequality. The Cauchy completion of A / I {\displaystyle A/I} in the norm

Stinespring dilation theorem (2,113 words) [view diff] exact match in snippet view article find links to article

positive semidefinite Hermitian sesquilinear forms satisfy the Cauchy–Schwarz inequality, the subset K ′ = { x ∈ K ∣ ⟨ x , x ⟩ K = 0 } ⊂ K {\displaystyle

Zermelo's navigation problem (2,010 words) [view diff] exact match in snippet view article find links to article

_{2}^{2}(\mathbf {d} _{1}\cdot \mathbf {w} )^{2}}{c^{6}}}} Using the Cauchy–Schwarz inequality, we obtain ( d 1 ⋅ d 2 ) 2 ≤ d 1 2 ⋅ d 2 2 {\displaystyle (\mathbf

Fréchet derivative (4,690 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \|h\|\to 0,\langle x,h\rangle \to 0} and because of the Cauchy-Schwarz inequality ⟨ x , h ‖ h ‖ ⟩ {\displaystyle \left\langle x,{\frac {h}{\|h\|}}\right\rangle

Marcum Q-function (7,425 words) [view diff] exact match in snippet view article find links to article

Q_{1}(a,b),\qquad \zeta >1.} Another such bound obtained via Cauchy-Schwarz inequality is given as e − b 2 / 2 ≤ Q n ( a , b ) ≤ 1 2 2 n − 1 2 + ζ 2