Let V be the vector space of all continuous complex-valued functions on the unit interval, 0 ? t ? 1. Prove that (f|g) = ?0 to 1 f(t)g(t)? dt is a valid inner product.
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An operation ⟨·,·⟩: V × V → ℂ (or ℝ for real vector spaces) is an inner product if for all u, v, w ∈ V and all scalars α ∈ ℂ (or ℝ), the following properties hold: Show more…
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