常见不等式

• \(|1 − e^{i\theta}| ≥ 2|\theta|/\pi\) whenever \(−\pi ≤ \theta ≤ \pi\)
• \(-log x\ge (1-x)/ln2\) where \(log\) has base \(2\).
• \(\left(\begin{array}{cccc} \Pi_{1} & 0 & \ldots & 0 \\ 0 & \Pi_{2} & \ldots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \ldots & \Pi_{M} \end{array}\right) \geq\left(\begin{array}{c} \Pi_{1} \\ \Pi_{2} \\ \vdots \\ \Pi_{M} \end{array}\right)\left(\Pi_{1} \Pi_{2} \ldots \Pi_{M}\right)\)