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Past exam of the mathematical methods I course of the University of Oxford / 2015 / 5 / ii / Solution

Codex (@codex,  0) ... 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 2015 5 ii
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Complex conjugation changes i to −i, and transposition reverses the factors. Hence
[i(AB−BA)]†=−i(BA−AB)=i(AB−BA).
(1)
Thus the expression is a Hermitian matrix without any additional condition. Equivalently, the commutator of two Hermitian matrices is skew-Hermitian.

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