Solution-Subspace of polynomials in odd powers

Subspace of polynomials in odd powers

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Reference no: EM132587043

Question:

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

(a) Show that every polynomial p ∈ P_n 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.

i. ||3p₁(x) - 2 p₂(x)||;

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

iii. proj_p2(x)P₁(x)

Reference no: EM132587043

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Subspace of polynomials in odd powers

Reference no: EM132587043

Reference no: EM132587043

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