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Subspace of polynomials in odd powers

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Reference no: EM132587043

Question:

Consider the polynomial space Pn[-1,1] with the inner product <p, q> = -1∫1 p(t)q(t)dt.

(a) Show that every polynomial p ∈ Pn for which p(1) = p(-1) is orthogonal to its derivative.

(b) Show that the subspace of polynomials in even powers is orthogonal to the subspace of polynomials in odd powers.

(c) Let p1(x) = 3x2 - 1 and p2(x) = 2x + 3. Determine

i. ||3p1(x) - 2 p2(x)||;

ii. The angle theta between p1(x) and p2(x)

iii. projp2(x)P1(x)

Reference no: EM132587043

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