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Orthogonal Projection of vector Y onto subspace S

  1. Oct 23, 2012 #1

    ElijahRockers

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    1. The problem statement, all variables and given/known data

    Let S be the linear span of the orthogonal set:

    {[3 2 2 2 2]T,[2 3 -2 -2 -2]T,[2 -2 3 -2 -2]T}

    Calculate the orthogonal projection of Y = [1 2 -1 3 1]T onto S.

    3. The attempt at a solution

    Not sure how to go about this...

    Do i find a vector that is orthogonal to S, and then project Y onto it?

    I dont have a book so any reference links would be helpful. I have watched numerous videos and read through paul's online notes but i cant seem to find anything about this problem. Exam tomorrow. :(
     
  2. jcsd
  3. Oct 23, 2012 #2

    ElijahRockers

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    I think I found it. If A is the matrix of the vectors spanning S, then the orthogonal projection of Y onto S is...

    A(ATA)-1ATY

    is that correct?
     
  4. Oct 23, 2012 #3
    Math 311? Im working on this one too
     
  5. Oct 23, 2012 #4

    ElijahRockers

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    Yep. Our teacher doesn't use visual or geometric examples at all, some it's all pretty abstract to me... I have been hitting the khan academy though so hopefully I'll be alright.
     
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