Results 1 to 4 of 4

Thread: projection matrix

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    37

    projection matrix

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

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

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

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

    However i dont now where to bring w into the problem
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    3
    Quote Originally Posted by Tekken View Post
    Let w = $\displaystyle \left(\begin{array}{ccc}-1\ \-1\ \-1\end{array}\right)$$\displaystyle
    $ Find the projection of w on space V.

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

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


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


    I worked out the projection matrix i.e. $\displaystyle A^T(A.A^T)^{-1}.A $ to be 3x3 matrix where $\displaystyle 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
    .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    37
    see below
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2010
    Posts
    37
    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

    $\displaystyle A^T(A.A^T)^{-1}.A
    $


    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix/projection of vectors problem
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: May 5th 2011, 10:53 AM
  2. Prove the Orthogonal Projection Matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Apr 13th 2011, 12:12 AM
  3. Projection Matrix
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Oct 30th 2010, 12:28 PM
  4. Non-symmetric matrix projection
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Jul 16th 2009, 05:24 AM
  5. Help with projection matrix!
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Jul 11th 2009, 05:48 AM

Search Tags


/mathhelpforum @mathhelpforum