Recovering eigenvalues from singular values [closed]

1. How are eigenvalues related to singular values?
2. Are singular values always eigenvalues?
3. Are singular values square root eigenvalues?

How are eigenvalues related to singular values?

For symmetric and Hermitian matrices, the eigenvalues and singular values are obviously closely related. A nonnegative eigenvalue, λ ≥ 0, is also a singular value, σ = λ. The corresponding vectors are equal to each other, u = v = x.

Are singular values always eigenvalues?

All real matrices have singular values, but non-square matrices don't have eigenvalues.

Are singular values square root eigenvalues?

Also, the singular values in S are square roots of eigenvalues from AA^T or A^TA. The singular values are the diagonal entries of the S matrix and are arranged in descending order. The singular values are always real numbers.