柯西不等式

$(a_{1}^{2} + a_{2}^{2}) (b_{1}^{2} + b_{2}^{2}) \geq (a_{1} b_{1} + a_{2} b_{2})^{2}$
方和积 大于等于 积和方

a_{i}, b_{i} \in R (i = 1, 2, \dots n) (a_{1}^{2} + a_{2}^{2} + ... + a_{n}^{2}) \cdot (b_{1}^{2} + b_{2}^{2} + ... + b_{n}^{2}) \geq (a_{1} b_{1} + a_{2} b_{2} + ... + a_{n} b_{n})^{2}

当且仅当 $\frac{a _{1}}{b _{1}} = \frac{a _{2}}{b _{2}} = \dots = \frac{a _{n}}{b _{n}}$ 取等

Quartz 4