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Let \(C[-1,1]\) be the real inner product space consisting of all continuous functions \(f:[-1,1] \rightarrow \mathbb{R}\), with the inner product \(\langle f, g\rangle:=\int_{-1}^{1} f(x) g(x) d x\).

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Let \(C[-1,1]\) be the real inner product space consisting of all continuous functions \(f:[-1,1] \rightarrow \mathbb{R}\), with the inner product \(\langle f, g\rangle:=\int_{-1}^{1} f(x) g(x) d x\). Let \(W\) be the subspace of odd functions, i.e. functions satisfying \(f(-x)=-f(x)\). Find (with proof) the orthogonal complement of \(W\).
in Mathematics by Platinum (102k points) | 444 views

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