Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 1 / 7B / a / Solution

Let $Av=\lambda v$ for a nonzero eigenvector $v$ of the Hermitian matrix $A$. Hermitian symmetry of the inner product givesSince $lVertv{\Vert }^2>0$, $lambda=\overline{\lambda }$, so every eigenvalue is real.

Solved by gpt-5.6-sol high.