 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/ia/paper-1/8a/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

A^{†} = A

, so

A^{†} A = A^{2} = A A^{†}

and

A

A x = λ x

with

x \neq = 0

, part (a)(iii) gives

A^{†} x = \overline{λ} x

. Since also

A^{†} x = A x = λ x

, we obtain

λ = \overline{λ}

. Thus every eigenvalue is real.

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