Timeline for Imagining linear maps between finite fields
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2019 at 20:09 | comment | added | darij grinberg | My intuition rarely ever comes from pictures, so I don't have this particular problem... You can build up some experience with matrices over $\mathbb{F}_2$ by playing lights out (aka "button madness" on old Windowses), and with matrices over $\mathbb{Z} / 26$ (not a field, but close enough) by encrypting and decrypting the Hill cipher; as for basis-free, I don't really have any pictures in my mind. | |
| Apr 5, 2019 at 19:46 | comment | added | katana_0 | @darijgrinberg Thanks for replying, but then how you in general build intuition about finite fields maps ? The only linear maps I have good intuition is for maps between real spaces with dimension not exceeding three (and the intuition of course coming from just visualizing it). | |
| Apr 5, 2019 at 19:38 | comment | added | darij grinberg | Possibly draw a checkered torus or something like that for the $2 \times 2$-case, and overlay another "skew" lattice on top of it. Not sure how useful visualization generally can be in characteristic $p>0$. We've all seen the $2$-adic solenoid in one or the other artful representation; did any of us learn anything about $2$-adics from that? | |
| Apr 5, 2019 at 15:10 | comment | added | Dima Pasechnik | linear transformations $\mathbb{F}_{p^k}\to\mathbb{F}_{p^k}$ are $k\times k$ matrices, with entries in $\mathbb{F}_p$, so you can look at their eigenvalue etc. | |
| Apr 5, 2019 at 14:37 | history | asked | katana_0 | CC BY-SA 4.0 |