Timeline for Fitting a simplex to set of almost orthogonal vectors
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7 at 14:59 | vote | accept | user103464 | ||
| Nov 29, 2023 at 21:14 | answer | added | David E Speyer | timeline score: 3 | |
| Nov 29, 2023 at 16:00 | comment | added | user103464 | Thanks a lot for fixing the Latex, somehow it wasn't displaying properly on my laptop so I removed it. So just restating what you said @fedja: there exists a set of vectors that are at pairwise distance $\sqrt 2 \pm O(1/d)$ but such that for any set of $d$ pairwise orthogonal vectors, there is one of the input vector at distance $O(1/\sqrt d)$? | |
| Nov 29, 2023 at 15:43 | comment | added | kodlu | @fedja, thanks; You're right for normalized vectors the Welch lower bound gives the bound stated in your comment. | |
| Nov 29, 2023 at 15:39 | comment | added | fedja | @kodlu I fixed the $\LaTeX$ :-) | |
| Nov 29, 2023 at 15:38 | history | edited | fedja | CC BY-SA 4.0 |
added 31 characters in body
|
| Nov 29, 2023 at 15:35 | comment | added | fedja | "such that each point of $S$ is mapped to a point in $Q$ at distance at most $O(1/d)$" That is too much to ask for. You cannot hope for a better bound than $O(1/\sqrt d)$ here. | |
| Nov 29, 2023 at 13:16 | comment | added | kodlu | Please use MathJax for your equations | |
| Nov 29, 2023 at 4:21 | history | asked | user103464 | CC BY-SA 4.0 |