Timeline for Is there a 'natural' projection from $O(n)$ into $S_n$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 17, 2022 at 20:34 | comment | added | Michael Hardy | For an orthogonal matrix, is there such a thing as the permutation matrix that is closest to it? (If so, that should do it.) | |
| Oct 17, 2022 at 19:29 | history | edited | Ben Deitmar | CC BY-SA 4.0 |
added 16 characters in body
|
| Oct 17, 2022 at 18:46 | answer | added | Christophe Leuridan | timeline score: 1 | |
| Oct 17, 2022 at 17:26 | comment | added | YCor | Using a Voronoi tiling you get 1,2,3 for free (define the projection arbitrarily on boundaries. However it's easily definable but maybe not easily computable. No idea about 4. | |
| Oct 17, 2022 at 17:26 | comment | added | Ben Deitmar | Thank you! Up to a measure zero is fine. | |
| Oct 17, 2022 at 15:59 | answer | added | Neil Strickland | timeline score: 3 | |
| Oct 17, 2022 at 14:58 | comment | added | David E Speyer | Does it really have to be defined for all $g \in O(n)$, or are you happy working up to a set of measure zero? If the latter, send any $g \in O(n)$ to the permutation $\sigma$ which maximizes $\sum_j g_{\sigma(j) j}$, discarding the matrices where ties occur. This is even rapidly computable, since it is an instance of maximum weight matching en.wikipedia.org/wiki/Maximum_weight_matching . | |
| Oct 17, 2022 at 14:27 | history | asked | Ben Deitmar | CC BY-SA 4.0 |