 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2015/5/ii/solution

i

- i

, and transposition reverses the factors. Hence

[i (A B - B A)]^{†} = - i (B A - A B) = i (A B - B A) .

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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