L.S.,
I am reading a paper of D. Blasius, where he states that the numbers Tr$(X^n) $ determine the conjugacy class of a semisimple element $X \in GL_n(\mathbb{C})$. I am having trouble proving this. I understand that for conjugate elements $A,B$ we have Tr$(A^n) =$ Tr$(B^n)$, it follows because $A = GBG^{-1}$ for some $G \in GL_n(\mathbb{C})$ and Tr$(AG) =$ Tr$(GA)$. But unfortunately I don't know how to go around the other way! Any help or hints would be greatly appreciated.
Many thanks,
Willem