Timeline for Representability of finite metric spaces
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 20, 2023 at 22:22 | comment | added | Bjørn Kjos-Hanssen | By the way, important to note that the matrix is $n\times n$ (and not $(n+1)\times (n+1)$) :) | |
| Oct 14, 2010 at 20:08 | comment | added | Suresh Venkat | It sounds like this merely reproves the characterization of embeddability in terms of Cayley-Menger determinants ? | |
| Jan 23, 2010 at 23:18 | vote | accept | Matt Noonan | ||
| Jan 21, 2010 at 8:25 | comment | added | Andrew Stacey | @Mariano: So I understand from the paper. @Tom: as a guess, then, Morgan's contribution was to extend from finite to arbitrary metric spaces. @Everyone else (since this attracted a vote against): My original intention was simply to leave a comment which made Hagen Knaf's answer a little more accessible, but then on reading the paper I decided that the result was simple enough to quote, hence the expansion of a comment into an answer. | |
| Jan 20, 2010 at 15:15 | comment | added | Tom Leinster | Andrew: the matrix you mention (let's call it $N$) is closely related to the matrix $M$ in my answer. By an elementary manipulation, your $N$ is positive semidefinite iff my $M$ is conditionally negative semidefinite. In fact, Schoenberg used this equivalence in the 1935 paper that I cited. | |
| Jan 20, 2010 at 12:46 | comment | added | Mariano Suárez-Álvarez | Hmm. I guess flat is non-negative determinants? | |
| Jan 20, 2010 at 12:43 | history | answered | Andrew Stacey | CC BY-SA 2.5 |