Timeline for Intersection of Subspaces with $O(3)$
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 26, 2016 at 17:51 | comment | added | Robert Bryant | While I can't correct it now, in my comment above, wherever I wrote $\mathrm{Gr}(3,6)$, I should have written $\mathrm{Gr}(6,9)$, i.e., the Grassmannian of $6$-dimensional subspaces of a $9$-dimensional subspace. | |
| Jan 26, 2016 at 17:45 | answer | added | Robert Bryant | timeline score: 3 | |
| Jan 26, 2016 at 17:23 | history | edited | YCor |
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| Jan 26, 2016 at 12:54 | comment | added | Matthias Ludewig | This would be the kind of answer I would be interested in. Is $U$ a dense subset? Probably one could characterize its complement by equations? I edited the post above. | |
| Jan 26, 2016 at 12:52 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
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| Jan 26, 2016 at 12:30 | comment | added | Robert Bryant | You should say what you mean by 'characterize'. The set of 6-dimensional subspaces of $\mathbb{R}^{3\times 3}$ is a compact manifold $\mathrm{Gr}(3,6)$ of dimension $18$, and it's clear (because of the examples already given) that the set of 6-dimensional spaces that don't meet $\mathrm{O}(3)$ is a (nonempty) open set $U\subset \mathrm{Gr}(3,6)$, so you are asking for a 'characterization' of an open subset in $\mathrm{Gr}(3,6)$. It can't be by equations, but maybe by some kind of inequality that defines the boundary of the set $U$ in $\mathrm{Gr}(3,6)$. Is that the sort of answer you seek? | |
| Jan 26, 2016 at 11:38 | review | Close votes | |||
| Jan 26, 2016 at 13:23 | |||||
| Jan 26, 2016 at 10:40 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
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| Jan 26, 2016 at 10:40 | answer | added | Roberto Pignatelli | timeline score: 4 | |
| Jan 26, 2016 at 10:36 | comment | added | user1688 | Take the subspace of matrices with first column equal to zero. | |
| Jan 26, 2016 at 10:34 | history | asked | Matthias Ludewig | CC BY-SA 3.0 |