Timeline for Properties of matrices changing with the parity of matrix dimension
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 11, 2018 at 15:30 | vote | accept | Widawensen | ||
| Dec 22, 2017 at 21:54 | answer | added | Mark Yasuda | timeline score: 1 | |
| Jul 15, 2017 at 15:45 | answer | added | ekkilop | timeline score: 1 | |
| Jul 15, 2017 at 15:29 | comment | added | ekkilop | "only even-dimensional skew-symmetric matrices can have full rank" - this of course extends to all matrices with eigenvalues appearing in $\pm$ pairs, e.g. skew-centrosymmetric matrices. | |
| Jun 21, 2017 at 9:57 | answer | added | PenasRaul | timeline score: 1 | |
| Jun 20, 2017 at 9:06 | history | edited | Widawensen | CC BY-SA 3.0 | added 288 characters in body |
| Jun 12, 2017 at 12:45 | history | edited | Widawensen | CC BY-SA 3.0 | added 238 characters in body |
| Jun 11, 2017 at 7:57 | history | edited | Widawensen | CC BY-SA 3.0 | added 41 characters in body |
| Jun 10, 2017 at 14:02 | comment | added | Widawensen | @D_S Very interested in.. all details are welcome.. | |
| Jun 10, 2017 at 13:58 | comment | added | D_S | Their root systems are in different classes. The "four classical semisimple groups" are $$\textrm{SL}_n, \textrm{Sp}_{2n}, \textrm{SO}_{2n}, \textrm{SO}_{2n+1}$$ so the odd and even orthogonal groups can be considered as different from each other as they are from $\textrm{SL}_n$. I can post a more detailed answer if you want. | |
| Jun 10, 2017 at 13:46 | comment | added | Widawensen | @D_S Yes, if they are quite different that is what I'm looking for, But what do you regarding as 'quite different' ? There is a difference between $n=2$ and $n=3$, but what is the general difference between odd and even $n$ ...? | |
| Jun 10, 2017 at 13:34 | comment | added | D_S | I don't know if this is really what you're looking for, but the groups of matrices $$\textrm{SO}_n(\mathbb{R}) = \{ x \in \textrm{GL}_n(\mathbb{R}) : xx^t = I \}$$ are quite different for $n$ even or odd. | |
| Jun 10, 2017 at 12:36 | history | undeleted | Widawensen | ||
| Jun 10, 2017 at 12:36 | history | deleted | Widawensen | via Vote | |
| Jun 10, 2017 at 10:56 | history | edited | Widawensen | CC BY-SA 3.0 | added 7 characters in body |
| Jun 10, 2017 at 10:49 | history | edited | Widawensen | CC BY-SA 3.0 | added 7 characters in body |
| Jun 10, 2017 at 10:39 | history | asked | Widawensen | CC BY-SA 3.0 |