Past exam of the mathematical methods I course of the University of Oxford / 2014 / 7 / iii

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- Solution iii

Solution

Every eigenvalue of a Hermitian matrix is real: if

He = λ e

with

e^{†} e = 1

, then

λ = e^{†} He = \overline{e^{†} He}

. Therefore

Im (λ_{1} λ_{2}) = 0.

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