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Inner Product Proof - Verify on L2[-1,1]
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[QUOTE="Ray Vickson, post: 4999947, member: 330118"] Write ##u(x) =x-x^2## and ##v(x) = 12 + x - 3x^3## as constant-coefficient linear combinations of ##p_0(x), p_1(x), p_2(x)##. You can do it using your instructor's hint, or you can do it for ##u(x)## the hard way, by getting three equations for ##a_0, a_1,a_2## from the identities ##u(x) = a_0 p_0(x) + a_1 p_1(x) + a_2 p_2(x) \; \forall x##. Do the same type of thing for ##v(x)##. Then, if you want to, you can verify explicitly that ##a_i = \langle u,p_i \rangle##, etc. [/QUOTE]
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Inner Product Proof - Verify on L2[-1,1]
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