 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2017-resit/10/a/ii/3/solution

A^{*} A = I

. For example,

A = (0 i i 0), A^{*} A = I .

This example is invertible, has nonreal off-diagonal entries, and preserves the standard Hermitian inner product. Although it is also symmetric, that additional property is not required for unitarity.

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