(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Relation between eigvals and singular vals.

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