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Math Help - Change these 2 vectors into an orthonormal set

  1. #1
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    Joined
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    Change these 2 vectors into an orthonormal set

    x1 =
    1
    1
    1
    1

    and x2 =
    1
    -1
    1
    -1

    Question: How can we change the set {x1,x2} into an orthonormal set? Demonstrate.

    Any help would be great!! Thanks
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  2. #2
    Member
    Joined
    Sep 2009
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    Thanks
    1
    Since the vectors are already orthoganal, all you do is 'normalize them. Ie divided each vector by its norm. For example, if x=(1,1,1,1) (transpose...), then the new vector is (1/||x||)x=(1/√(4))x=(1/2)x= (1/2,1/2,1/2,1/2).
    You do the other one.
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