Group Theory in a Nutshell 笔记

线性代数复习

关于迹的恒等式

设\(M\)可对角化为\(\Lambda\), 则\(M=S^{-1}\Lambda S\), 本征值为\(\lambda_{a},a=1,2\cdots n\), 则$\operatorname{tr}\qty(\ln M)=\operatorname{tr}\qty(\ln (S^{-1}\Lambda S))=\operatorname{tr}\qty(\ln S^{-1})+\operatorname{tr}\qty(\ln \Lambda)+\operatorname{tr}\qty(\ln S)=\operatorname{tr}\qty(\ln \Lambda)=\sum_{a}\ln \lambda a =\ln $