 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-1/2c/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Apply part (b) to the normal matrix

C = D - λ I

. Since

(D - λ I) e = 0

, one has

(D^{†} - \overline{λ} I) e = C^{†} e = 0.

Thus $e$ is an eigenvector of $D^{†}$ with eigenvalue $\overline{λ}$ .

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