Timeline for Eigenvalues of permutations of a real matrix: can they all be real?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Sep 16, 2013 at 14:30 | answer | added | Wolfgang | timeline score: 2 | |
| Aug 11, 2013 at 11:50 | answer | added | S. Carnahan♦ | timeline score: 6 | |
| Aug 9, 2013 at 23:41 | answer | added | Igor Rivin | timeline score: 1 | |
| Jul 10, 2013 at 19:40 | history | edited | Wolfgang | CC BY-SA 3.0 |
added 6x6 matrix with c(M)=9
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| Jul 5, 2013 at 7:34 | comment | added | Wolfgang | for $c(I_n)$, each cycle of length $d$ in a permutation contributes [(d-1)/2] conjugate pairs. $c(I_5)=118$ is correct. | |
| Jul 5, 2013 at 7:33 | comment | added | Wolfgang | You are right for the first 3x3 one. I don't know what happened. Maybe a simple typo. Did you check my other ones? | |
| Jul 4, 2013 at 22:38 | answer | added | Felix Goldberg | timeline score: 0 | |
| Jul 4, 2013 at 21:09 | comment | added | Felix Goldberg | I also get $c(I_{5})=8$ so this is all very odd - perhaps I am missing something? | |
| Jul 4, 2013 at 20:50 | comment | added | Felix Goldberg | This is an interesting question but I have some trouble reproducing the examples. For instance, if I take the $3 \times 3$ matrix in the first example I get $c(M)=4$ instead of zero. (If you change places between the 1st and the 3rd rows, you get a matrix whose char. poly. is $x^{3}-x^{2}+2x-2$ which has two non-real roots. There is also another pair of non-real eigenvalues). Perhaps there is a bug in the OP's program. | |
| Jul 4, 2013 at 19:43 | history | edited | Wolfgang | CC BY-SA 3.0 |
added Update 2
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| Jun 4, 2013 at 20:19 | comment | added | Suvrit | Wow, impressive! | |
| Jun 4, 2013 at 20:18 | history | edited | Wolfgang | CC BY-SA 3.0 |
added a nice 4x4 one and found a 5x5 one with c(M)=0!
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| May 23, 2013 at 21:18 | history | edited | Wolfgang | CC BY-SA 3.0 |
added remark for n=4
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| May 23, 2013 at 20:58 | history | asked | Wolfgang | CC BY-SA 3.0 |