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Math Help - projection matrix

  1. #1
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    projection matrix

    Let w = \left(\begin{array}{ccc}-1\ \-1\ \-1\end{array}\right)<br />
Find the projection of w on space V.

     V = <\left(\begin{array}{ccc} 1\ \ 4\ \ 0\end{array}\right)\left(\begin{array}{ccc} 1\ \ -1\ \ 2\end{array}\right)>

    I've already found  V^{perp}  = the span of \left(\begin{array}{ccc} -4\ \ 1\ \ -1\end{array}\right)

    I worked out the projection matrix i.e.  A^T(A.A^T)^{-1}.A to be 3x3 matrix where  A = \left(\begin{array}{ccc} -4\ \ 1\ \ -1\end{array}\right)

    However i dont now where to bring w into the problem
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  2. #2
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    Quote Originally Posted by Tekken View Post
    Let w = \left(\begin{array}{ccc}-1\ \-1\ \-1\end{array}\right) <br />
Find the projection of w on space V.

     V = <\left(\begin{array}{ccc} 1\ \ 4\ \ 0\end{array}\right)\left(\begin{array}{ccc} 1\ \ -1\ \ 2\end{array}\right)>

    I've already found  V^{perp}  = the span of \left(\begin{array}{ccc} -4\ \ 1\ \ -1\end{array}\right)


    This can't possibly be correct since (1\,-\!\!1\,\,2)\cdot (-4\,\,1\,-\!\!1)\neq 0 ....check your work: it must be V^{\perp}=Span\{(-8\,2\,5)\}


    I worked out the projection matrix i.e.  A^T(A.A^T)^{-1}.A to be 3x3 matrix where  A = \left(\begin{array}{ccc} -4\ \ 1\ \ -1\end{array}\right)


    ?? How a matrix with one single row is a 3x3 matrix? What did you actually mean here?

    Tonio


    However i dont now where to bring w into the problem
    .
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  3. #3
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    see below
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  4. #4
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    Ooops sorry my bad, multiplied wrong

    I wasn't saying the single row matrix was a 3x3 matrix... i was simply saying that i used the single row matrix to calculate the projection matrix (a 3x3) matrix using the formula

    A^T(A.A^T)^{-1}.A<br />


    As my latex knowledge is still poor, it would have taken me too long to write out the 3x3 matrix...

    Anyways thanks for pointing out my error in part 1 of the question
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