Show that the subgradient of the nuclear norm is given by $$\partial|X| = UV^T + W$$ where $X = U \Sigma V^T $ is the compact SVD of $X$, $W$ is a matrix such that $U^T W = 0$ and $WV = 0$, and $\|W\|_2 \le 1$.
This is exact that question. But I don't know how to get $W$. Can some explain that paper explicitly?
