Cauchy's Inequality

Theorem

 * $\displaystyle \sum {r_i^2} \sum {s_i^2} \ge \left({\sum {r_i s_i}}\right)^2$

where all of $r_i, s_i \in \R$.

Also known as
This result is also known as the Cauchy-Schwarz Inequality, although that name is also given to the more general Cauchy-Bunyakovsky-Schwarz Inequality.