Timeline for What is the hidden symmetry behind four generic planes in $\mathbb{R}^4$?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2019 at 16:46 | vote | accept | Dustin G. Mixon | ||
| Nov 9, 2019 at 16:46 | comment | added | Dustin G. Mixon | Ah, put another way, four generic planes can be linearly transformed to take the form $\operatorname{span}\{e_1,e_2\}$, $\operatorname{span}\{e_3,e_4\}$, $\operatorname{span}\{e_1+e_3,e_2+e_4\}$, and $\operatorname{span}\{e_1+ae_3,e_2+be_4\}$ for some distinct nonzero $a$ and $b$. These planes are preserved by transforms of the form $\operatorname{diag}(x,y,x,y)$ for nonzero $x$ and $y$. | |
| Nov 8, 2019 at 10:58 | comment | added | Ben McKay | To be more precise, over $\mathbb{Z}/2\mathbb{Z}$ you can't get distinct nonzero eigenvalues, so for any field but that one the argument works. | |
| Nov 8, 2019 at 9:40 | history | answered | Ben McKay | CC BY-SA 4.0 |