Results 1 to 4 of 4

Math Help - Find the orthogonal projection of a vector

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    15

    Find the orthogonal projection of a vector

    Find the orthogonal projection of \vec{v} on the span[\vec{v_{1}},\vec{v_{2}},\vec{v_{3}}]


    \vec{v}=(6,3,9,6) , \vec{v_{1}}=(2,1,1,1) , \vec{v_{2}}=(1,0,1,1) , \vec{v_{3}}=(-2,-1,0,-1) ;

    \vec{v},\vec{v_{1}},\vec{v_{2}},\vec{v_{3}} \in \mathbb{R}^{4} .

    Can you please tell me how to do this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Find the orthogonal projection of a vector

    One way: find an orthonormal basis \{e_1,e_2,e_3\} of \textrm{Span}[v_1,v_2,v_3] . The solution is p=<v,e_1>e_1+<v,e_2>e_2+<v,e_3>e_3 .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: Find the orthogonal projection of a vector

    Another way: find a vector \vec w perpendicular to each of \vec v_1, \vec v_2, \vec v_3.

    The solution is \vec p = \vec v - {\langle \vec v,\vec w \rangle \vec w \over \langle \vec w,\vec w \rangle}.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2011
    Posts
    15

    Re: Find the orthogonal projection of a vector

    Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 2nd 2011, 02:20 PM
  2. Find the orthogonal projection
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 13th 2011, 01:10 PM
  3. Find the standard matrix of an orthogonal projection
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 24th 2010, 06:21 AM
  4. Find orthogonal projection
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 12th 2010, 08:44 PM
  5. find the orthogonal projection
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: June 9th 2007, 01:16 AM

/mathhelpforum @mathhelpforum