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Results tagged with cauchy-schwarz-inequality
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user 2083
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.
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A plausible inequality
Here is a proof for the case $n=2$:
Some general facts: As Douglas pointed out, one can assume $a_1=1, a_n=0$. Also, note that the RHS is:
$$(\sum x_i^2)(\sum y_i^2) -(\sum x_iy_i)^2 = \sum_{i<j}(x …
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