For a linear map $T:V\to V$ where $V$ is a finite dimensional inner product space over $\mathbb{C}$, I know the result $\chi_{T^*}=\overline{\chi_T}$ (where $T^*$ is the adjoint map for $T$). My problem is I can't find a proof for it... Do you know one?
Also, I'm guessing we can also prove $m_{T^*}=\overline{m_T}$, but again, can't find a proof anywhere or generate one myself...
Can you help me please? I really don't see...
(here $\chi$ is for characteristic polynomial and $m$ for the minimal one)