Past exam of the mathematical methods I course of the University of Oxford / 2016 resit / 9 / i

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- Solution i

Solution

Both expressions are the same scalar:

u^{T} v = i \sum u_{i} v_{i} = i \sum v_{i} u_{i} = v^{T} u .

This identity uses the ordinary transpose and remains true for complex entries. A Hermitian inner product uses a conjugate transpose instead and has conjugate symmetry, not this bilinear symmetry.

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