# Subgradient of nuclear norm [duplicate]

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?

https://math.stackexchange.com/users/10117/lepidopterist

• Please provide some more context behind this question: Is there something in particular you are struggling with? What have you tried? Why are you interested in this? – Kitter Catter Mar 3 '17 at 2:04
• I could get the $UV^T$ , but I don't know how to get W – Kevin Z Mar 3 '17 at 2:25
• When asking for an explanation of "that paper explicitly", it surely makes sense to give a citation to the paper with title, author, journal, and date. – hardmath Mar 3 '17 at 21:24
• This is exact that question, but I don't know how to get W. And I hope some one could explain that paper concerning this . Characterization of the Subdifferential of Some Matrix Norms – Kevin Z Mar 3 '17 at 22:11