 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-1/7b/b/solution

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

e_{i}

G

and set

u_{i} = e_{i}

v_{i} = A e_{i} / λ_{i}

. Part (a) shows that the

v_{i}

H

. If

U

and

V

have these vectors as columns, then they are unitary and

V^{†} A U = diag (λ_{1}, \dots, λ_{n}) .

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