Tag: 特殊线性群

Theorem 1. 假设$A(t)$是$n\times n$的单参数$n$阶方阵, $t\in(-\epsilon,\epsilon)$. 若$A(t)$是由$X(t)$生成的, 即满足 \[ A'(t)=X(t)A(t),\quad\forall t\in(-\epsilon,\epsilon), \] 则 \[ \left( \det A(t) \right)’=\mathrm{tr}\left( X(t) \right)\det A(t). \]