V is the space of polynomials with real coefficients with degree ≤ n.
The inner product is defined like this: <p,q> = the integral from -1 to 1 of pq(x)
I need to prove that if: p ≠ 0, <p,x^i> = 0, i < k then: deg p ≥ k
Thanks for any kind of help
V is the space of polynomials with real coefficients with degree ≤ n.
The inner product is defined like this: <p,q> = the integral from -1 to 1 of pq(x)
I need to prove that if: p ≠ 0, <p,x^i> = 0, i < k then: deg p ≥ k
Thanks for any kind of help
By contradiction, assume then belongs to the subspace of the polynomials of degree less or equal to , which is generated by: .
But is orthogonal to each of the elements of a set that generates it, hence it must be the polynomial ! contradiction!
now : hence