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Linear Algebra: Orthogonal Projections

  1. Mar 19, 2012 #1
    Hey first time poster here.

    1. The problem statement, all variables and given/known data

    Find the orthogonal projection projWy

    u1 = [-1; 3; 1; 1], u2 = [3; 1; 1; -1], u3 = [-1; -1; 3; -1], y = [1; 0; 0; 1]

    where {u1, u2, u3} is an orthogonal basis.

    2. Relevant equations

    yhat = [dot(y,U1)/dot(U1,U1)]U1 + ....... [dot(y,Un)/dot(Un,Un)]Un

    3. The attempt at a solution

    I used the equation above and I ended up getting:

    0u1 + 1/6[3; 1; 1;-1] + 1/6[-1; -1; 3; -1] = 1/6[2; 0; 4; -2]

    the answer given by my professor is 1/6[-1; -1; 3; -1] and I don't understand why. I can get that answer by not adding dot(y,U3)/dot(U3,U3)]U3 to yhat, but I suspect that isn't the right way to do it. Where am I going wrong?
     
  2. jcsd
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