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Math Help - Modified QR factorization

  1. #1
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    Question Modified QR factorization

    Any help with this question would be greatly appreciated

    Let u be a unit vector and define Qu = I - 2uuT (the T means transpose)

    Show that Qu is symmetric and orthogonal, furthermore show that

    (Qu)^2 = I

    Thanks
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  2. #2
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    Quote Originally Posted by Algebah View Post
    Any help with this question would be greatly appreciated

    Let u be a unit vector and define Qu = I - 2uuT (the T means transpose)

    Show that Qu is symmetric and orthogonal, furthermore show that

    (Qu)^2 = I

    Thanks
    There is no analytic trickery here. For symmetry, just show (I - 2uu^T)^T = (I - 2uu^T) by performing the operations (recall (AB)^T = B^T A^T). Likewise show (I - 2uu^T)(I - 2uu^T) = I. Those imply orthogonality, which is Q^T Q = Q Q^T = I.
    Last edited by JakeD; May 24th 2007 at 12:48 AM.
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  3. #3
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    Smile

    Thankyou very much
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