Results 1 to 5 of 5

Math Help - Orthogonal Complements of a Subspace of Polynomials (LaTex notation)

  1. #1
    Junior Member
    Joined
    Nov 2011
    Posts
    45

    Orthogonal Complements of a Subspace of Polynomials (LaTex notation)

    img.top {vertical-align:15%;}  R_{2}[x] , and let S be the subspace of all polynomials p(x) satisfying

    \\ \frac{\2d^2\p}{dx^2} = p(2)

    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  R_{2}[x] , and let S be the subspace of all polynomials p(x) satisfying

    \\ \frac{\2d^2\p}{dx^2} = p(2)

    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.

    " />
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,391
    Thanks
    758

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

    use [tex] instead of [tex]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

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

    Quote Originally Posted by maxgunn555 View Post
    Let V be  \mathbb{R}_{2}[x] , and let S be the subspace of all polynomials p(x) satisfying

    \displaystyle \frac{d^2p}{dx^2} = p(2)

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

    \langle p,q\rangle = 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.
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Nov 2011
    Posts
    45

    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).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

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

    Quote Originally Posted by maxgunn555 View Post
    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).
    Right, so you have an equation. A polynomial p(x)\in S^\perp if and only if p(-1)q(-1)+p(0)q(0)+p(1)q(1)=0 for every q(x)=ax^2+bx+c such that 4a=4a+2b+c, right>
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orthogonal Complements
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: June 27th 2010, 01:36 PM
  2. Orthogonal Complements
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 20th 2010, 05:10 PM
  3. orthogonal complements and dimension
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: July 5th 2008, 09:35 PM
  4. Orthogonal complements
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: April 29th 2008, 12:02 AM
  5. orthogonal complements
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 22nd 2008, 04:29 PM

Search Tags


/mathhelpforum @mathhelpforum