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Math Help - Finding the projection

  1. #1
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    Finding the projection

    Hello,

    Can someone please help me figure out the projection for this?

    projw x, where x = (1,2,0,-1) W is the subspace of R^4 spanned by the vectors.

    v1 = (1/2,1/2,1/2,1/2)
    v2 = (1/2,1/2,-1/2,-1/2)
    v3 = (1/2,-1/2,1/2,-1/2)

    Thanks!
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  2. #2
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    Project_{~\vec{v}}~\vec{x} = <\vec{x},\vec{v}>\displaystyle\frac{\vec{v}}{\|\ve  c{v}\|}

    \mathfrak{B}_W = span(\vec{v}_1,~\vec{v}_2,~\vec{v}_3)

    Project_{~W}~\vec{x}=\sum\limits_{i=1}^3 Project_{~\vec{v}_i}~\vec{x}=\displaystyle\frac{1}  {2}\left[\begin{array}{c} 3\\ 3\\ -1\\ -1 \end{array}\right]
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  3. #3
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    can you elaborate more on the 3rd line?
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