待解問題 – 數學絲路

n 個向量所夾的「立體」體積必不大於各邊長的總乘積

$\left|\begin{matrix} a_{11} & a_{12} & \ldots & a_{1n} \\a_{21} & a_{22} & \ldots & a_{2n} \\\vdots & \vdots & & \vdots\\a_{n1} & a_{n2} & \ldots & a_{nn}\end{matrix} \right|^2\leq \left(a_{11}^2+a_{12}^2+ \cdots+ a_{1n}^2 \right)\left(a_{21}^2+a_{22}^2+ \cdots+ a_{2n}^2 \right)\cdots\left(a_{n1}^2+a_{n2}^2+ \cdots+ a_{nn}^2 \right)$