# Relation between eigvals and singular vals.

1. Sep 21, 2008

### Pacopag

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 $$\lambda$$ satisfy $$Ax=\lambda x$$ where x are the eigenvectors.
Singular values $$\sigma$$ satisfy $$\sqrt{A^H A} v = \sigma v$$,
i.e. singular values of A are the eigenvalues of the matrix $$\sqrt{A^H A}$$

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