The Cauchy–Schwarz inequality is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector ... Hermann Schwarz · Kantorovich inequality · Hölder's inequality · Titu's lemma |
Cauchy-Schwarz is an inequality with many ubiquitous formulations in abstract algebra, calculus, and contest mathematics. |
The Cauchy-Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, states that for all sequences of real numbers a i a_i ai and b i ... |
Thus the Cauchy-Schwarz inequality is an equality if and only if u is a scalar multiple of v or v is a scalar multiple of u (or both; the phrasing has been ... |
Let U=X−EXσX,V=Y−EYσY. Then EU=EV=0, and Var(U)=Var(V)=1. Using the Cauchy-Schwarz inequality for U and V, we obtain |EUV|≤√E[U2]E[V2]=1. But note that EUV=ρ(X, ... |
The Cauchy-Schwarz inequality may be regarded as one of the most impor- tant inequalities in mathematics. It has many names in the literature: Cauchy-. Schwarz, ... |
The Cauchy-Schwarz inequality is fundamental to many areas of mathematics, physics, engineering, and computer science. We introduce and motivate this inequality ... |
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