Timeline for Integrating matrix maps
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2018 at 18:32 | comment | added | Deane Yang | good question. I don’t know | |
| Feb 13, 2018 at 13:02 | comment | added | Igor Rivin | @DeaneYang Yes, of course. Does it mean that every image can be reparametrized? | |
| Feb 13, 2018 at 10:27 | answer | added | Deane Yang | timeline score: 4 | |
| Feb 13, 2018 at 10:03 | comment | added | Deane Yang | the map $f$ matters, not just its image. | |
| Feb 13, 2018 at 5:35 | comment | added | Igor Rivin | @DeaneYang third partials of the mysterious $g?$ So, what does this translate to for the data ($f$)? That $\frac{\partial f_{ij}}{x_k} = \frac{\partial f_{ik}}{x_j}?,$ plus the symmetry of the matrix? (the latter needed to go from $h$ to $g$). This is somehow unsatisfying, because it is not very geometric to me - if I have a disk sitting in $S^{n\times n}$ (symmetric matrices), how do I tell a disk which comes from such a construction from one which does not?! | |
| Feb 13, 2018 at 5:10 | comment | added | Deane Yang | But you don’t get a debauche of integrability conditions. If you write down all of the equations that $g$ and $h$ need to satisfy, the only integrability condition needed is that third partials commute. The proof is essentially the same as for the Poincaré Lemma. | |
| Feb 13, 2018 at 1:42 | history | asked | Igor Rivin | CC BY-SA 3.0 |