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Consider the inner product space $$\langle f,g \rangle= \int_{-1}^{1} f(x) g(x) \ dx $$

find the non zero orthogonal function with respect to $f(x)=1$ in the subspace span of ${1,e^{x}}$ ?

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  • $\begingroup$ hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question. $\endgroup$ – Ahmad Bazzi Jan 31 '19 at 19:26
  • $\begingroup$ -1 to 1 is the interval. can you add it too? $\endgroup$ – Allic Mendonca Jan 31 '19 at 19:27
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If you compute the orthogonal projektion $P(e^x)$ on span(1). Then $e^x - P(e^x)$ is in the orthogonal complement of span(1).

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