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Homework Help: Projections on subspaces

  1. Jan 4, 2008 #1
    [SOLVED] Projections on subspaces

    1. The problem statement, all variables and given/known data
    I have some questions on this topic:

    1) If I have an orthonormal basis for a subspace U and I have a vector A, and I want to find the orthogonal projection of A onto U, then I use the expression written here:


    2) If I have found the orthogonal complement V to U, and I wish to find the projection of the vector A onto V, I can either:

    - use the expression in http://mathworld.wolfram.com/VectorSpaceProjection.html on the orthonormal set that spans V

    - or use A - proj(U)_A (the projection of A onto U)

    3) I don't know if this is "legal", but I would like to draw your attention to my question in: https://www.physicsforums.com/showthread.php?t=207060

    3. The attempt at a solution
    Can you guys confirm this? Sadly, in my book it is not written that well.

    Thanks in advance,

    sincerely Niles.
  2. jcsd
  3. Jan 4, 2008 #2


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    Homework Helper

    Yes, that's correct.
  4. Jan 4, 2008 #3
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