Timeline for $\arg\max$ in the dual norm of the nuclear norm
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 10, 2020 at 0:14 | vote | accept | Santiago Armstrong | ||
| May 3, 2020 at 20:46 | comment | added | Santiago Armstrong | Thanks! You are absolutely right! I will add a proof here in case someone is looking for it in the future: Suppose $X^*=uv^*$ where $u$ and $v$ are the left and right singular vectors of $M$ associated with the largest singular value. To show that $X^*$ attains the optimum, it suffices to show that $\langle M, X^*\rangle = \|M\| = \sigma_{max}$. But this follows from the cyclicity of the trace: $trace(M^*uv^*) = trace(V^*\Sigma U u v^*) = trace(v^*V^*\Sigma U u) = \sigma_{max}$ | |
| May 3, 2020 at 14:27 | history | edited | alesia | CC BY-SA 4.0 |
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| May 3, 2020 at 13:31 | history | answered | alesia | CC BY-SA 4.0 |