Question: Show that the 2n + 1 complex exponentials eikx for k = - n, - n + 1........ - 1, 0, 1,... ,n, form an

Show that the 2n + 1 complex exponentials eikx for k = - n, - n + 1........ - 1, 0, 1,... ,n, form an orthonormal basis for the space of complex-valued trigonometric polynomials under the Hermitian inner product

f, g) = f(x) g(x)dx

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Applied Linear Algebra 1st edition by Peter J. Olver, Cheri Shakiban