Timeline for Checking the generic rank of a matrix
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2022 at 8:41 | comment | added | Vladimir Dotsenko | @YCor this might help a lot, thanks! (Due to many situations where I work with $S_n$-modules, I tend to ignore the usefulness of modular arithmetic even where it is useful!!) | |
| Oct 24, 2022 at 8:20 | comment | added | YCor | You can also work (this is how I usually do) modulo a "random" prime number $\ell$ (say with 3 or 4 digits) and one "random" value of $t$. The advantage of working modulo $\ell$ is that you avoid producing large entries/denominators. If the rank is indeed $r$, this will quite likely provide the answer $r$ (which certifies the expected rank is $\ge r$), and you can repeat the request with other values only if it provides rank $<r$. | |
| Oct 24, 2022 at 7:24 | comment | added | Vladimir Dotsenko | @QiaochuYuan that does not make me completely happy but is definitely worth considering, thanks! | |
| Oct 24, 2022 at 7:17 | comment | added | Qiaochu Yuan | Are you happy with a probabilistic algorithm? If so, choosing random values of $t$ and row reducing should work with high probability, right? | |
| Oct 24, 2022 at 7:12 | history | asked | Vladimir Dotsenko | CC BY-SA 4.0 |