Timeline for Computing a determinant involving roots of unity
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Oct 23, 2017 at 9:00 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Slightly shortened already-bumped question.
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| Oct 23, 2017 at 4:54 | review | Suggested edits | |||
| S Oct 23, 2017 at 9:00 | |||||
| Jun 24, 2017 at 17:56 | answer | added | efs | timeline score: 8 | |
| Jun 24, 2017 at 16:27 | answer | added | T. Amdeberhan | timeline score: 5 | |
| Jun 24, 2017 at 12:52 | vote | accept | deterroot | ||
| Jun 24, 2017 at 12:00 | comment | added | Sylvain JULIEN | Thank you very much but there's no magic behind this, it's just a matter a familiarity with numbers. | |
| Jun 24, 2017 at 11:36 | comment | added | Uri Bader | This is all very nice, but I am really amazed by how @SylvainJULIEN got his heuristic out of a three experiments datum. | |
| Jun 23, 2017 at 23:00 | answer | added | GH from MO | timeline score: 35 | |
| S Jun 23, 2017 at 22:28 | history | suggested | Peter Mortensen | CC BY-SA 3.0 |
Copy edited.
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| Jun 23, 2017 at 21:46 | review | Suggested edits | |||
| S Jun 23, 2017 at 22:28 | |||||
| Jun 23, 2017 at 19:54 | answer | added | Federico Poloni | timeline score: 10 | |
| Jun 23, 2017 at 18:10 | answer | added | Neil Strickland | timeline score: 17 | |
| Jun 23, 2017 at 17:38 | comment | added | Sylvain JULIEN | Maybe just a coincidence, but still :$ \vert\Delta(2)\vert=2^{2/2} $ , $ \vert\Delta(3)\vert=3^{3/2} $ , $ \vert\Delta(4)\vert=4^{4/2} $ , so you can try to check whether $ \vert\Delta(n)\vert=n^{n/2} $ or not. | |
| Jun 23, 2017 at 16:55 | comment | added | efs | I computed the determinant $\Delta(3)$ with a variable $x$ replacing $\xi$ and it can be factorized; it gives $x(x+1)(x-1)^3$. Maybe you can get a simple expression in general, using a Mathematica or any math software. | |
| Jun 23, 2017 at 15:55 | review | Close votes | |||
| Jun 23, 2017 at 21:05 | |||||
| Jun 23, 2017 at 15:39 | comment | added | deterroot | That's what I've been trying to do but I didn't succeed. Could you give some more details? Thanks Federico | |
| Jun 23, 2017 at 15:37 | comment | added | Federico Poloni | Looks like you can obtain this matrix starting from the Fourier matrix (Vandermonde on roots of unity) and doing a few elementary row operations to subtract the all-ones first row from every other row. This should give you a method to reduce this determinant to the Vandermonde one. | |
| Jun 23, 2017 at 15:32 | review | First posts | |||
| Jun 23, 2017 at 15:34 | |||||
| Jun 23, 2017 at 15:32 | history | asked | deterroot | CC BY-SA 3.0 |