Timeline for Frobenius inner product of a zero line-sum matrix and a doubly stochastic matrix
Current License: CC BY-SA 4.0
14 events
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| Jun 15, 2020 at 20:14 | history | undeleted | Lo Celso | ||
| Jun 15, 2020 at 18:10 | history | deleted | Lo Celso | via Vote | |
| Jun 15, 2020 at 17:47 | history | edited | Lo Celso | CC BY-SA 4.0 |
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| Jun 15, 2020 at 17:43 | comment | added | Lo Celso | @dohmatob Thanks for your advice! I used Sage to try the $3 \times3$ case and I found that the Birkhoff polytope, with the additional property I required on $B$ (I let $S=\{(i,i)\}$), has 24 vertices, which is indeed hard to analyze. I have changed the question to a weaker one which I believe is true. | |
| Jun 15, 2020 at 17:39 | history | edited | Lo Celso | CC BY-SA 4.0 |
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| Jun 15, 2020 at 8:06 | comment | added | dohmatob | Going beyond your two examples, a computer might be of help finding potential counterexamples here. Data enters the problem in a very combinatorial way, and it's hard to get an intuition for why the statement should be true in general. So my 2 cents would be to try to finding some genuine counterexamples (e.g using a computer), and only in case of failure to find such, should you have more confidence in the claim, and try proving it. | |
| Jun 14, 2020 at 23:48 | history | edited | Lo Celso | CC BY-SA 4.0 |
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| Jun 14, 2020 at 23:32 | comment | added | Lo Celso | @JochenGlueck Thanks! I miswrote it because I was thinking about minimizing $\langle A,B\rangle_F$ over a Birkhoff polytope. | |
| Jun 14, 2020 at 23:30 | history | edited | Lo Celso | CC BY-SA 4.0 |
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| Jun 14, 2020 at 23:07 | comment | added | Jochen Glueck | A small correction: $B$ is called a doubly stochastic matrix, not a Birkhoff polytope. The Birkhoff polytope is the set of all doubly stochastic matrices (in fixed dimension). | |
| Jun 14, 2020 at 21:12 | history | edited | Lo Celso | CC BY-SA 4.0 |
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| Jun 14, 2020 at 21:12 | history | undeleted | Lo Celso | ||
| Jun 14, 2020 at 21:09 | history | deleted | Lo Celso | via Vote | |
| Jun 14, 2020 at 21:06 | history | asked | Lo Celso | CC BY-SA 4.0 |