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Let $A$ be a positive semidefinite matrix. Are there any bounds known for the $q$-th moment of the $p$-th Schatten norm of matrix $A$? Here, $1 \leq p,q \leq \infty$.

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put on hold as unclear what you're asking by Dima Pasechnik, Chris Godsil, LSpice, Sean Lawton, Yemon Choi Jul 19 at 5:12

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  • $\begingroup$ Bounds in terms of what? And when you say moment, do you just mean "power"? Normally moments are averages of powers, but here it is not clear what you are trying to average $\endgroup$ – Yemon Choi Jul 12 at 23:19
  • $\begingroup$ In terms of the pth Shatten norm. $\endgroup$ – user124297 Jul 14 at 2:43
  • $\begingroup$ Your response doesn't seem to answer my question. Clearly the qth moment of the pth Schatten norm is bounded by ... the qth moment of the pth schatten norm. But clearly this is not what you mean. Can you please give us an example of what you want, with actual values of p or q $\endgroup$ – Yemon Choi Jul 14 at 3:06
  • $\begingroup$ Also, can you please explain what you mean by $q$th moment? Please actually give a definition in the style of a book or a paper $\endgroup$ – Yemon Choi Jul 14 at 3:07