Timeline for A log inequality for positive definite trace-one matrices
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Feb 1, 2017 at 19:23 | history | edited | Ludwig | CC BY-SA 3.0 |
Added link to follow-up problem.
|
| Mar 24, 2016 at 9:48 | vote | accept | Ludwig | ||
| Mar 23, 2016 at 11:47 | answer | added | Fedor Petrov | timeline score: 9 | |
| Mar 21, 2016 at 21:36 | answer | added | Fedor Petrov | timeline score: 6 | |
| Mar 20, 2016 at 22:07 | comment | added | Fedor Petrov | It looks probable (and holds for $n=2$). | |
| Mar 20, 2016 at 22:02 | history | edited | Ludwig | CC BY-SA 3.0 |
Minor corrections
|
| Mar 19, 2016 at 7:49 | comment | added | Fedor Petrov | For $N=2$ this reduces (If I am not mistaken) to equivalent inequality $(\sum a_i^2)(\sum b_i^2)+(\sum a_ib_i)^2\geqslant \sqrt{(\sum a_i^4)(\sum b_i^4)}+\sum a_i^2b_i^2$ for arbitrary reals $a_i,b_i$. | |
| Mar 18, 2016 at 14:31 | comment | added | Iosif Pinelis | Without loss of generality, $X^{1/2}$ is a diagonal matrix with positive $c_1,\dots,c_n$ on the diagonal such that $\sum_{k=1}^n c_k^2=1$. Letting then $v_i=[v_{i1},\dots,v_{in}]^T$ and $y_{ik}:=v_{ik}\sqrt{c_k}(\sum_{q=1}^n c_q^2v_{iq}^2)^{-1/2}$, one rewrites $(*)$ as $\prod_{i=1}^N\sum_{j=1}^N(\sum_{k=1}^n y_{ik}y_{jk})^2\ge N^N$ given that $\sum_{k=1}^n c_k^2=\sum_{k=1}^n c_k y_{ik}^2=1$ for all $i=1,\dots,N$. Then one could perhaps use Lagrange multipliers. | |
| Mar 18, 2016 at 11:10 | history | edited | Ludwig | CC BY-SA 3.0 |
Added a comment on the problem.
|
| Mar 17, 2016 at 23:16 | vote | accept | Ludwig | ||
| Mar 17, 2016 at 23:24 | |||||
| Mar 14, 2016 at 7:44 | history | edited | Ludwig | CC BY-SA 3.0 |
Corrected error
|
| Mar 13, 2016 at 22:11 | history | edited | Ludwig | CC BY-SA 3.0 |
Corrected a typo
|
| Mar 13, 2016 at 20:50 | history | asked | Ludwig | CC BY-SA 3.0 |