 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-1/7b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Let

A v = λ v

for a nonzero eigenvector

v

A

. Hermitian symmetry of the inner product gives

λ ∥ v ∥^{2} = (v, A v) = (A v, v) = \overline{λ} ∥ v ∥^{2} .

Since

l V er t v ∥^{2} > 0

l amb d a = \overline{λ}

, so every eigenvalue is real.

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