Orthogonal Complements of a Subspace of Polynomials (LaTex notation)

img.top {vertical-align:15%;}
, and let S be the subspace of all polynomials p(x) satisfying

Find the orthogonal complement of S with respect to the inner product

<p,q> = p(-1)q(-1) +p(0)q(0) + p(1)q(1)

And find the polynomial in S which is closest to 1 + x _ x^2

Thanks for any help.

" alt=" Let V be , and let S be the subspace of all polynomials p(x) satisfying

Find the orthogonal complement of S with respect to the inner product

<p,q> = p(-1)q(-1) +p(0)q(0) + p(1)q(1)

And find the polynomial in S which is closest to 1 + x _ x^2

Thanks for any help.

" />

Re: Orthogonal Complements of a Subspace of Polynomials (LaTex notation)

use [tex] instead of [tex]

Re: Orthogonal Complements of a Subspace of Polynomials (LaTex notation)

Quote:

Originally Posted by

**maxgunn555** Let

be

, and let

be the subspace of all polynomials

satisfying

Find the orthogonal complement of

with respect to the inner product

And find the polynomial in

which is closest to

Thanks for any help.

I believe this is the question. I now feel like you should show some work. Tell us where you are stuck, because this is a computation. So, what part of the setup don't you understand?

Re: Orthogonal Complements of a Subspace of Polynomials (LaTex notation)

Hi again, i attempted it a few days ago before moving onto other modules i have. but i know the orthogonal complement is a space where each vector is orthogonal to each vector in the subspace S. orthogonal meaning the inner product of two vectors if orthogonal to each other equal zero (or pi).

Re: Orthogonal Complements of a Subspace of Polynomials (LaTex notation)