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Projections along N

  1. Jul 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Let R={[x,y,z,w]:x=y and z=w} and N={[x,y,z,w]:x=-y and z=-w}
    Find the rule in standard coordinates for the projection of R4x1 onto R along N


    2. Relevant equations



    3. The attempt at a solution
    I have B wrt R as {[1,1,0,0],[0,0,1,1]} and B wrt N as {[1,-1,0,0], [0,0,1,-1]}, so my basis is {[1,1,0,0],[0,0,1,1],[1,-1,0,0],[0,0,1,-1]}.
    [E]B=
    [1 0 0 0
    0 1 0 0
    0 0 0 0
    0 0 0 0]

    I used my basis as my Q^(-1), so
    Q=
    [.5 .5 0 0
    0 0 .5 .5
    .5 -.5 0 0
    0 0 .5 -.5]
    which gives me
    Q^(-1)[E]BQ=
    [.5 .5 0 0
    .5 .5 0 0
    0 0 .5 .5
    0 0 .5 .5]
    so my rule would be
    E[x =
    y
    z
    w]

    [x+y
    x+y
    z+w
    z+w]

    but,
    E[1 =
    1
    0
    0]

    [2
    2
    0
    0]

    instead of
    [1
    1
    0
    0]

    but
    E[1 =
    -1
    0
    0]

    [0
    0
    0
    0]
    which is correct

    my Q^(-1) can't be right, but i'm not sure how to find another one.
     
  2. jcsd
  3. Jul 17, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Sorry, but I find this impossible to read!
     
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