I am confused with the statement "The characteristic feature of the SVD promises that as $\sigma_i$ decreases, the singular vectors $u_i$ and $v_i$ become more and more oscillatory", which is in my assignment of solving ill-posed problems.
I understand $v_i$ is mapped to $u_i$ and its stretching(or shrinking) factor is the singular value $\sigma_i$. I don't know how it is related to oscillation of the vectors. Does it has any connection with frequency?