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Math Help - Vector projection question

  1. #1
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    Vector projection question

    I have a vector v orthogonal to [w1 w2 w3]. Is it possible to get the projection of v to the space spanned by W=[w1 w2 w3 w4] without calculating the inverse of W^tW?
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  2. #2
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    If v is already orthogonal to w1, w2, and w3, its projection onto that subspace is just its projection onto w4. I don't know if that involves "calculating the inverse of W^tW" because I don't know what " W^tW" means for W a vector space.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    If v is already orthogonal to w1, w2, and w3, its projection onto that subspace is just its projection onto w4. I don't know if that involves "calculating the inverse of W^tW" because I don't know what " W^tW" means for W a vector space.
    W is the basis of the space. I was thinking to get the projection of v to W, I need to use W(W^tW)^{-1}W^tv. Could you please give a brief proof of "If v is already orthogonal to w1, w2, and w3, its projection onto that subspace is just its projection onto w4". Sorry for my ignorance. I am not a math guy.
    Last edited by brakepad; September 28th 2010 at 08:07 AM. Reason: wrong typing
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