 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2016-resit/9/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.

 New to topics? Read the docs here!