Timeline for Vandermonde matrix is totally positive
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Dec 5, 2019 at 20:44 | history | edited | Sam Hopkins |
edited tags
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| Nov 3, 2017 at 6:37 | comment | added | Loïc Teyssier | I gave a definition at the beginning of the question. It is not related to positive definiteness (see Wikipedia). | |
| Nov 2, 2017 at 22:50 | comment | added | Ali Taghavi | But just a question. Are you considering a particular definition of "positivity"? The standard one required the symetricity of our matrix. This is not the case for the vandermond matrix | |
| Nov 2, 2017 at 11:51 | comment | added | Loïc Teyssier | @AliTaghavi: actually, this proof is not mine but is due to A. Glutsyuk, who really was the person looking for references :) | |
| Nov 2, 2017 at 6:19 | comment | added | Loïc Teyssier | By induction. You order the entries like this: $x_1<x_2<\cdots<x_n$, then introduce the variable $x_1=:h$ and set $x_j=:\hat{x}_j+h$ for all $j>1$. By differentiating enough time with respect to $h$ you end up with a Vandermonde of size smaller by $1$, which is positive by hypothesis. | |
| S Nov 1, 2017 at 5:53 | history | suggested | Ali Taghavi |
I add two tags.
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| Nov 1, 2017 at 3:58 | comment | added | Ali Taghavi | (+1) For this interesting question. May I ask you to include the sketch of your variational proof, in your question. Thank you. | |
| Nov 1, 2017 at 3:54 | review | Suggested edits | |||
| S Nov 1, 2017 at 5:53 | |||||
| Oct 31, 2017 at 20:41 | answer | added | darij grinberg | timeline score: 9 | |
| Oct 31, 2017 at 18:06 | answer | added | Fedor Petrov | timeline score: 6 | |
| Oct 31, 2017 at 17:41 | answer | added | Harry Richman | timeline score: 13 | |
| Oct 31, 2017 at 17:39 | vote | accept | Loïc Teyssier | ||
| Oct 31, 2017 at 16:57 | answer | added | john mangual | timeline score: 11 | |
| Oct 31, 2017 at 16:48 | history | asked | Loïc Teyssier | CC BY-SA 3.0 |