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Using QR decomposition to find a nontrivial solution to Ax=0

  1. Apr 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Supposedly the process to solve Ax=0 is to solve Transpose(R).Ry=z (where z is a random vector) and then x=y/(norm-2 of y).


    2. Relevant equations



    3. The attempt at a solution

    Ay=b for some random vector b

    Transpose(A).Ay= Transpose(A).b

    Transpose(QR).QRy=Transpose(A).b

    Transpose(R).Transpose(Q).QRy = z where z is Transpose(A).b

    Transpose(R).Ry=z since Q is orthogonal

    Then x (the solution to the homogeneous system) is y/(norm-2 y)? But why?
     
    Last edited: Apr 5, 2009
  2. jcsd
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