 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2016/11/a/ii/solution

The conjugate transpose also reverses factor order. If

U

and

V

(U V)^{†} (U V) = V^{†} U^{†} U V = V^{†} I V = I .

Thus their product is unitary. This is closure under multiplication in the unitary group.

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