 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2004/ib/paper-4/11e/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

The adjoint reverses products, so for the two Hermitian operators

(α β)^{*} = β^{*} α^{*} = β α .

Thus $α β$ is Hermitian if and only if $α β = β α$ . No positivity hypothesis is needed for this equivalence.

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