The following inequality is named after Augustin Louis Cauchy (1789 - 1857) and Hermann Amandus Schwarz (1843 - 1921).
Let $x_1,x_2,\ldots x_n$ and $y_1,y_2,\ldots y_n$ be real numbers. Then the sum of absolute values of the products $\sum _{i=1}^{n}|x_{i}y_{i}|$ can be estimated from above by the so-called Cauchy-Schwarz inequality $$\sum _{i=1}^{n}|x_{i}y_{i}|\leq \left(\sum _{i=1}^{n}x_{i}^{2}\right)^{\frac 12}\left(\sum _{i=1}^{n}y_{i}^{2}\right)^{\frac 12}.$$
Proofs: 1
Proofs: 1
