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Math Help - Singular value decomposition

  1. #1
    MHF Contributor alexmahone's Avatar
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    Singular value decomposition

    Suppose A is a 2 by 2 symmetric matrix with unit eigenvectors u_1 and u_2. If its eigenvalues are 3 and -2, what are the matrices U, \sum, V' in its SVD?

    ( V' is the transpose of V.)
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint

    The eigenvalues of A^hA are 9 and 4 so, the singular values of A are 3 and 2 .
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by FernandoRevilla View Post
    Hint

    The eigenvalues of A^hA are 9 and 4 so, the singular values of A are 3 and 2 .
    Thanks. So I get:



    Is that right?
    Last edited by alexmahone; April 17th 2011 at 05:48 AM.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by alexmahone View Post
    Is that right?

    Using the standard method, the factorization is


    [ u_1, -u_2 ]^t A [ u_1, u_2 ] = diag [ 3, 2 ]
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  5. #5
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by FernandoRevilla View Post
    Using the standard method, the factorization is


    [ u_1, -u_2 ]^t A [ u_1, u_2 ] = diag [ 3, 2 ]
    Are you saying that my answer in post #3 is wrong? (Sorry for being so slow; I'm self studying Linear Algebra from Strang and he isn't very clear most of the time.)
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by alexmahone View Post
    Are you saying that my answer in post #3 is wrong? (Sorry for being so slow; I'm self studying Linear Algebra from Strang and he isn't very clear most of the time.)

    Your answer is right. I also provided the matrix U , that is


    V = [ u_1, - u_2] , U = [ u_1 , u_2 ]
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