The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the inner product between two vectors in an inner...

Cauchy's inequality may refer to: the Cauchy–Schwarz inequality in a real or complex inner product space Cauchy's inequality for the Taylor series coefficients...

Among other things, Schwarz improved the proof of the Riemann mapping theorem, developed a special case of the Cauchy–Schwarz inequality, and gave a proof...

other. The special case p = q = 2 gives a form of the Cauchy–Schwarz inequality. Hölder's inequality holds even if ‖fg‖1 is infinite, the right-hand side...

Azuma's inequality Bernoulli's inequality Bell's inequality Boole's inequality Cauchy–Schwarz inequality Chebyshev's inequality Chernoff's inequality Cramér–Rao...

\operatorname {E} [Z])^{1/2}} by the Cauchy–Schwarz inequality. The desired inequality then follows. ∎ The Paley–Zygmund inequality can be written as P ⁡ ( Z >...

Kantorovich inequality is a particular case of the Cauchy–Schwarz inequality, which is itself a generalization of the triangle inequality. The triangle...

including infinite-dimensional examples. The triangle inequality follows from the Cauchy–Schwarz inequality as follows: Given vectors u {\displaystyle u} and...

{\displaystyle \operatorname {R} _{XX}(0)} is always real. The Cauchy–Schwarz inequality, inequality for stochastic processes:: p.392  | R X X ⁡ ( t 1 , t 2...

The Cauchy-Schwarz inequality for complex random variables, which can be derived using the Triangle inequality and Hölder's inequality, is | E ⁡...

In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting...

{\displaystyle n=1} this is the theorem in one variable). By the Cauchy–Schwarz inequality, the equation gives the estimate: | f ( y ) − f ( x ) | ≤ | ∇...

In stochastic calculus, the Kunita–Watanabe inequality is a generalization of the Cauchy–Schwarz inequality to integrals of stochastic processes. It was...

prove the Cauchy–Schwarz inequality. The AM–GM inequality is also known for the variety of methods that can be used to prove it. Jensen's inequality states...

{\displaystyle \langle a,b\rangle =\rho (b^{\ast }a).} Thus from the Cauchy–Schwarz inequality we have | ρ ( b ∗ a ) | 2 ≤ ρ ( a ∗ a ) ⋅ ρ ( b ∗ b ) . {\displaystyle...

to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several...

{\displaystyle \log(x).} Cauchy–Schwarz inequality – Mathematical inequality relating inner products and norms Hölder's inequality – Inequality between integrals...

to the final result. Titu's lemma, a direct consequence of the Cauchy–Schwarz inequality, states that for any sequence of n {\displaystyle n} real numbers...

Bunyakovsky conjecture), and is credited with an early discovery of the Cauchy–Schwarz inequality, proving it for the infinite dimensional case as well as for definite...

In mathematics, the van der Corput inequality is a corollary of the Cauchy–Schwarz inequality that is useful in the study of correlations among vectors...

tensor Cauchy–Hadamard theorem Cauchy horizon Cauchy identity Cauchy index Cauchy inequality Cauchy's integral formula Cauchy's integral theorem Cauchy interlacing...

y\in K^{n}{\text{ with }}\|x\|_{2}=\|y\|_{2}=1\}.} Proved by the Cauchy–Schwarz inequality. ‖ A ∗ A ‖ 2 = ‖ A A ∗ ‖ 2 = ‖ A ‖ 2 2 {\textstyle...

dx\right)^{1/q}.} For p = q = 2, Hölder's inequality becomes the Cauchy–Schwarz inequality. Minkowski inequality. Suppose that p ≥ 1 is a real number and...

consequence of Cauchy–Bunyakovsky–Schwarz inequality. Nevertheless, in his article (1997) Sedrakyan has noticed that written in this form this inequality can be...

= sub(x)'*sub(y); complex p?dotc dotc = conjg(sub(x)')*sub(y) Cauchy–Schwarz inequality Cross product Dot product representation of a graph Euclidean...

j})-\prod _{j=1}^{d}z_{i}} is the discrepancy function. Applying the Cauchy–Schwarz inequality for integrals and sums to the Hlawka–Zaremba identity, we obtain...

and differentiation operations commute (second condition). The Cauchy–Schwarz inequality shows that var ⁡ ( T ) var ⁡ ( V ) ≥ | cov ⁡ ( V , T ) | = | ψ...

property is ultimately a consequence of the more fundamental Cauchy–Schwarz inequality, which asserts | ⟨ x , y ⟩ | ≤ ‖ x ‖ ‖ y ‖ {\displaystyle \left|\langle...

}}\right)\,dx=1.} Squaring the expression in the integral, the Cauchy–Schwarz inequality yields 1 = ( ∫ [ ( θ ^ − θ ) f ] ⋅ [ f ∂ log ⁡ f ∂ θ ] d x ) 2...

particularly useful inequality to analyze homomorphism densities is the Cauchy–Schwarz inequality. The effect of applying the Cauchy-Schwarz inequality is "folding"...