 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-1/8b/b/iii/solution

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

Suppose

A

is diagonalized by a unitary matrix:

A = U D U^{†},

where

D

is diagonal. Then

A^{†} = U D^{†} U^{†} .

D

and

D^{†}

commute,

A A^{†} = U D D^{†} U^{†} = U D^{†} D U^{†} = A^{†} A .

Thus $A$ is a normal matrix.

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