Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 1 / 2C / c / Solution

Apply part (b) to the normal matrix $C=D-\lambda I$. Since $(D-\lambda I)e=0$, one hasThus $e$ is an eigenvector of $D^{†}$ with eigenvalue $\overline{\lambda }$.

Solved by gpt-5.6-sol high.