What's the minimal polynomial of a normal endomorphism $\phi$ with eigenvalues $2, 2, 1+i, 1+i, 1-i, 1-i, 3$?
It is $\mu_\phi | (t-2)^2(t-1-i)^2(t-1+i)^2(t-3)$ but is there any more I can derive from the fact that $\phi \circ \phi^*=\phi^* \circ \phi$?