Timeline for A generalized log inequality for positive definite trace-one matrices
Current License: CC BY-SA 3.0
23 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 12, 2017 at 16:59 | vote | accept | Ludwig | ||
| Feb 12, 2017 at 10:26 | answer | added | jjcale | timeline score: 3 | |
| Feb 4, 2017 at 9:43 | history | edited | Ludwig | CC BY-SA 3.0 |
Corrected typo
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| Feb 4, 2017 at 9:31 | history | edited | Ludwig | CC BY-SA 3.0 |
Corrected typo
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| Feb 2, 2017 at 19:01 | comment | added | jjcale | Easy to show for $n = m$ . | |
| Feb 1, 2017 at 19:13 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Feb 1, 2017 at 16:57 | comment | added | Suvrit | The question looks really nice. I wish I had some more time to think about it. One brute-force approach may be to minimize the $\log\det$ part wrt $X>0$ under the constraint $\text{tr}(X)=1$, to see if the optimality conditions lead to any simplification. Alternatively, To use Schur complements to be able to trigger the induction. Not sure if these ideas are helpful at all though! | |
| Feb 1, 2017 at 15:54 | comment | added | Ludwig | Yes, sorry. I edited the question in order to fix it. | |
| Feb 1, 2017 at 15:53 | history | edited | Ludwig | CC BY-SA 3.0 |
Edited attempt of solution.
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| Jan 30, 2017 at 17:49 | history | edited | Ludwig | CC BY-SA 3.0 |
Edited attempt of solution.
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| Jan 30, 2017 at 16:45 | comment | added | Suvrit | why the 'exp' in there?? | |
| Jan 29, 2017 at 21:37 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Jan 29, 2017 at 20:55 | comment | added | Suvrit | Because this is essentially an inequality about determinants $\mathrm{tr}(\log Z) = \log\det(Z)$, I am still hopeful that it will work out. | |
| Jan 29, 2017 at 20:40 | comment | added | Ludwig | @Suvrit: Induction doesn't seem to me a viable way to solve the problem. In particular, in the inductive step $m-1\to m$ I don’t see how to decouple the inequality in order to apply Fedor’s argument for $m=1$ (the presence of the matrix logarithm and inverse make this task hard). However it's very possible that I’m mistaken. | |
| Jan 29, 2017 at 20:07 | comment | added | Suvrit | Did you try a simple induction on $m$ to reuse Fedor's proof? | |
| Jan 29, 2017 at 15:50 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Jan 29, 2017 at 9:45 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Jan 29, 2017 at 9:39 | history | edited | Ludwig | CC BY-SA 3.0 |
Added attempt of solution.
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| Jan 28, 2017 at 20:12 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Jan 28, 2017 at 13:32 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Jan 28, 2017 at 10:57 | history | edited | Ludwig | CC BY-SA 3.0 |
Corrected typo
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| Jan 28, 2017 at 10:31 | history | asked | Ludwig | CC BY-SA 3.0 |