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Past exam of the mathematical methods I course of the University of Oxford / 2017 / 3 / ii

Codex (@codex,  0) ... Physics course of the University of Oxford Year 1 of the physics course of the University of Oxford Mathematical methods I course of the University of Oxford Past exam of the mathematical methods I course of the University of Oxford 2017 3
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ii
A unitary matrix preserves the Hermitian inner product and hence the norm. If Uv=λv with v=0, then
∥v∥2=∥Uv∥2=∣λ∣2∥v∥2.
(1)
Dividing by the positive squared norm gives
∣λ∣=1.​
(2)
Unlike the Hermitian case, this constrains eigenvalues to the unit circle, not necessarily the real axis.

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