Timeline for Ways to prove an inequality
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2010 at 13:00 | comment | added | Suvrit | Hmm, the first idea that comes to my mind is: use $\varphi(x) = 1/(1+|x|)$ is a positive-definite function (it is in fact infinitely divisible), which itself can be proved using $|x|$ is conditionally negative-def. (though proving the latter might require a simple integral!); | |
| Sep 28, 2010 at 19:20 | comment | added | Gjergji Zaimi | How would you prove the posdef of L? | |
| Sep 28, 2010 at 7:47 | comment | added | Suvrit | Minor comment about your first example, it is "easily" seen to be nonnegative, because it is the sum of all entries of the positive-definite matrix: $B = aa^T \circ L$, where $L_{ij} = 1/(1+|i-j|)$ and $\circ$ denotes the Hadamard product. The only semi-trivial part is to prove posdef of $L$, but that can be done in numerous ways, the more advanced of which might use an integral representation. | |
| Jul 9, 2010 at 14:30 | vote | accept | CommunityBot | ||
| Jul 9, 2010 at 0:17 | history | answered | Gjergji Zaimi | CC BY-SA 2.5 |