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The Cauchy-Schwarz inequality states $|\langle x,y \rangle |\leq ||x||\cdot ||y||.$ Use this tag for questions related to the CS inequality and its applications.

5 votes

A plausible inequality

The following proof is a bit heavy-handed; I'm sure you it can be simplified. Assume $a_1=1, a_n=0$ as suggested above and write: Write $$F(x,y) = \sum_{i=1}^n a_i(x_i^2-y_i^2)$$, $$G(x,y)=F(x,y)^2+ …
Lior Silberman's user avatar