Question: Let H be a linear space with inner product (-, ) and corresponding norm || - ||. Let S E H and u E H.

Let H be a linear space with inner product (-, ) and corresponding norm || - ||. Let S E H and u E H. Prove that u* E S is the best approximation of u within S if and only if 'U,* is the orthogonal projection of u onto 8 that is (uu*,v) =0 V'UES. Hint: You may want to use the function f(t) = \"u (215* + tv)||2

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