Hi, can someone shed some light on the following question. It's been bothering me for a while and I'd like to know where I went wrong. Here is what I can remember of the question.(adsbygoogle = window.adsbygoogle || []).push({});

The following is an inner product for polynomials in P_3(degree <= 3): [tex]\left\langle {f,g} \right\rangle = \int\limits_{ - 1}^1 {f\left( x \right)g\left( x \right)} dx[/tex]

Let W be the subspace of the vector space P_3, spanned by {x^2, x^3}.

Find the orthogonal projection of a polynomial [tex]p\left( x \right) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 \in P_3 [/tex] onto W. Find also the polynomial [tex]q\left( x \right) \in W[/tex] which minimises the integral [tex]\int\limits_{ - 1}^1 {\left( {3 + 5x - q\left( x \right)} \right)^2 } dx[/tex].

I think that q(x) is some kind of projection onto W. I kind of drew an analogy with 'distance' when I did this question. But obviously something's wrong with that approach. Does anyone have suggestions as to how to find q?

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# Homework Help: Subspaces and inner products

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