Results 1 to 4 of 4

Math Help - Find the projection of the function

  1. #1
    Junior Member
    Joined
    Oct 2012
    From
    Ohio
    Posts
    48

    Find the projection of the function

    Let V = C([-1,1]), with the inner product <f,g> = ∫-1,1 f(t)g(t) dt,

    and let W be the subspace R<=2[x] ⊂ V, with basis the Legendre polynomials {1, x, 3x2-1}.

    Find the projection of the function f(t) = et onto W using this basis.


    I am completely lost there is too much going on in this problem.. and my professor never really explained projections with integrals, or legendre polynomials, etc. Any help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Find the projection of the function

    Hey TimsBobby2.

    Remember that your final vector will be v(t) = a_t*a + b_t*b + c_t*c and if (a,b,c) are orthogonal to each other then a_t is the inner product of the function against the vector a that is normalized, with the same for b and c respectively.

    First figure out the normalized vectors (if they aren't already normalized) and take the inner product of your function with respect to those vectors.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2012
    From
    Ohio
    Posts
    48

    Re: Find the projection of the function

    Would I use the legendre polynomials to figure out the normalized vectors? That's where I'm having the trouble I suppose. I'm not sure what to use to begin.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Find the projection of the function

    If they are orthogonal, then they will be the vectors. Normalizing them is just dividing by SQRT(<v,v>) like you do with normal vectors. If this term is 1, then they are normalized.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Find the formula for the projection on W along U?
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: August 3rd 2011, 05:53 AM
  2. Find the orthogonal projection
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 13th 2011, 12:10 PM
  3. Find orthogonal projection
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 12th 2010, 07:44 PM
  4. Find the projection of a vector
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 27th 2009, 01:11 AM
  5. find the orthogonal projection
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: June 9th 2007, 12:16 AM

Search Tags


/mathhelpforum @mathhelpforum