Let two polynomials p, g, p ( x i ) g ( x i ) , i 0, 1, , n on a,b Let Pk be the polynomial space of degree k or less Explain why , is not an inner product in Pk, when k n (I understand if k is less than or equal to n, then is an inner product, but I could not see why this becomes invalid when k n, please explain to me in details )

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Question: Let two polynomials p, g, = p ( x i ) g ( x i ) , i = 0, 1, ..., n on [a,b]

Let two polynomials p, g,

= p(xi)g(xi) , i = 0, 1, ..., n on [a,b]

Let Pk be the polynomial space of degree k or less.

Explain why < , > is not an inner product in Pk, when k > n

(I understand if k is less than or equal to n, then <> is an inner product, but I could not see why this becomes invalid when k > n, please explain to me in details.)

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