\(n\) 阶行列式的定义

\[ \begin{vmatrix} a_{11} & a_{21} & \cdots & a_{n1} \\ a_{12} & a_{22} & \cdots & a_{n2} \\ \vdots & \vdots & \ddots & \vdots \\ a_{1n} & a_{2n} & \cdots & a_{nn} \\ \end{vmatrix} = \sum_{p \in S_n} (-1)^{t(p)} \prod_{i=1}^n a_{p_i} \]