 Solution

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

H

H^{†} = H

. Reversing the product of

n

identical factors has no effect, so

(H^{n})^{†} = (H^{†})^{n} = H^{n} .

Hence every positive integer power is Hermitian. The identical-factor condition matters; a product of different Hermitian matrices need not be Hermitian.

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