Timeline for How hard (P, NP, NP-hard) is it to compute Schur norms of matrices (as multipliers)?
Current License: CC BY-SA 3.0
11 events
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| Jul 17 at 15:40 | comment | added | Nathaniel Johnston | For cross-referencing's sake, this answer was used and cited in our recent paper arXiv:2206.02863. | |
| May 21, 2014 at 1:59 | comment | added | Nathaniel Johnston | Note that the above code is actually based on the SDP in Section 3.2 of arXiv:1207.5726. I imagine they both simplify down similarly though. Not sure if it might be possible to simplify further and even find an explicit formula in certain special cases. | |
| May 21, 2014 at 1:57 | comment | added | Suvrit | Thanks for posting the code; it looks amazingly simple! This encourages me to read the Watrous paper and play with the SDP. | |
| May 21, 2014 at 1:54 | comment | added | Nathaniel Johnston | Suvrit: Yep, I implemented the SDP in MATLAB. I've now posted code above, which actually simplifies really nicely after using the fact that these maps have such a special form. | |
| May 21, 2014 at 1:52 | history | edited | Nathaniel Johnston | CC BY-SA 3.0 |
Added MATLAB code
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| May 21, 2014 at 0:55 | comment | added | Suvrit | Nathaniel: did you implement the SDP for computing this? if so, could you share that script? thanks! | |
| May 20, 2014 at 2:13 | comment | added | Nathaniel Johnston | Good point. It is indeed the case that equality holds -- this is proved in Theorem 8.7 of Paulsen's book (ref. [15] of the Davidson paper). | |
| May 20, 2014 at 1:55 | comment | added | Suvrit | very nice find! Btw, does the Thm tell that the Schur multiplier norm is equal to the 'cb' norm---it seems a brief extra argument is needed... | |
| May 19, 2014 at 23:51 | history | edited | Nathaniel Johnston | CC BY-SA 3.0 |
added more examples
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| May 19, 2014 at 23:46 | history | edited | Nathaniel Johnston | CC BY-SA 3.0 |
added example
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| May 19, 2014 at 23:38 | history | answered | Nathaniel Johnston | CC BY-SA 3.0 |