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Relation between eigvals and singular vals.

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Is there a way to get the eigenvalues of a matrix from its singular values?


    2. Relevant equations
    Eigenvalues [tex]\lambda[/tex] satisfy [tex]Ax=\lambda x[/tex] where x are the eigenvectors.
    Singular values [tex]\sigma[/tex] satisfy [tex]\sqrt{A^H A} v = \sigma v[/tex],
    i.e. singular values of A are the eigenvalues of the matrix [tex]\sqrt{A^H A}[/tex]


    3. The attempt at a solution
    It seems that
    [tex]\lambda = \pm \sqrt{\sigma}[/tex]
    but this only gives some of the eigenvalues. How do I get the others?
     
  2. jcsd
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