Timeline for Determinantal inequality for difference of substochastic matrices
Current License: CC BY-SA 4.0
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| Jul 30 at 13:19 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| S Jul 25 at 13:45 | history | bounty ended | Abdelmalek Abdesselam | ||
| S Jul 25 at 13:45 | history | notice removed | Abdelmalek Abdesselam | ||
| Jul 20 at 5:32 | answer | added | Toni Mhax | timeline score: 1 | |
| Jul 18 at 19:51 | history | edited | LSpice | CC BY-SA 4.0 |
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| Jul 18 at 19:29 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| S Jul 17 at 14:59 | history | bounty started | Abdelmalek Abdesselam | ||
| S Jul 17 at 14:59 | history | notice added | Abdelmalek Abdesselam | Draw attention | |
| Jul 14 at 10:55 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Jul 11 at 11:57 | comment | added | darij grinberg | Ah, Proposition 2.4, I see! I should have waited until that page. | |
| Jul 11 at 11:57 | comment | added | darij grinberg | Yes, and the converse is even easier. My restatement has the advantage(?) of looking like a linear analogue of the Hadamard inequality, but I'm not sure if this advantage is anything more than aesthetic. | |
| Jul 11 at 11:57 | comment | added | Abdelmalek Abdesselam | @darijgrinberg: in section 2 I explain from scratch these equivalences around the notion of IFDZ, and do so in a very explicit way. | |
| Jul 11 at 11:55 | comment | added | Abdelmalek Abdesselam | One can reduce to the case $\forall i,j$, $\min(A_{ij},B_{ij})=0$ and then indeed show the equivalence with your reformulation. | |
| Jul 11 at 11:55 | comment | added | darij grinberg | Incidentally, your work is great and I'm reading it right now! Just wondering whether the equivalence (in the middle of page 3) between $\mathcal{R}$ being an IFDZ and $\widehat{\mathcal{R}}^{\mathbb{E}}$ being identically zero is supposed to be obvious at that point, or if it is meant to be proved later. (It looks to me like a restatement of the Proposition in §6 of Al-Amrani's Introduction, which however isn't fully obvious.) | |
| Jul 11 at 11:48 | comment | added | darij grinberg | I would restate this inequality (which is nice and new to me!) as follows: If $M$ is a real $n\times n$-matrix, then $\left|\det M\right| \leq \prod_{i=1}^n \omega_i\left(M\right)$, where $\omega_i\left(M\right)$ is the maximum absolute value of a sum of a sub-tuple of the $i$-th row of $M$. | |
| Jul 11 at 11:43 | history | asked | Abdelmalek Abdesselam | CC BY-SA 4.0 |