How smooth are the singular values of a matrix $F$ in terms of entries of $F$? I am hoping for Lipschitz continuity, but was not able to find it.



Lipschitz continuity of singular values
The singular values of $F$ are the (square roots of ) eigenvalues of $F F^t,$ and the regularity of the latter have been studied half-to-death. See either T. Kato (perturbation theory of linear operators, ch. 1) or Golub-van Loan (Matrix Computations -- they almost certainly talk about singular values directly, without going through eigenvalues, but at worst talk about eigenvalues).


