Timeline for Geometric proof of the Vandermonde determinant?
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2015 at 21:48 | answer | added | Fedor Petrov | timeline score: 1 | |
| Sep 2, 2015 at 21:15 | answer | added | Josefina Alvarez | timeline score: 2 | |
| May 15, 2014 at 7:37 | answer | added | Zurab Silagadze | timeline score: 3 | |
| May 7, 2014 at 10:40 | answer | added | Geoff Robinson | timeline score: 4 | |
| May 7, 2014 at 5:38 | answer | added | K1. | timeline score: 1 | |
| Nov 8, 2013 at 19:46 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
replaced deprecated tag 'geometry' since question was recently edited
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| Mar 7, 2011 at 21:06 | history | edited | Daniel Litt | CC BY-SA 2.5 |
Added a reference to another proof
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| Dec 2, 2010 at 12:01 | answer | added | Ben Krause | timeline score: 3 | |
| Jun 25, 2010 at 11:03 | answer | added | Tom Goodwillie | timeline score: 10 | |
| Jun 25, 2010 at 3:18 | answer | added | Ian Agol | timeline score: 3 | |
| Jun 24, 2010 at 13:42 | comment | added | Daniel Litt | Well, my motivation is that the row-reduction proof makes the geometry really obvious---essentially, row reduction finds a volume-preserving linear transformation that turns the parallelepiped defined by the Vandermonde matrix into a rectangular prism. I'd just like to have a more synthetic proof. | |
| Jun 24, 2010 at 13:20 | comment | added | Wadim Zudilin | Thanks, Daniel, for clarification: you'd like to have some "measure" interpretation of the involved polynomials rather than view them as defining algebraic curves/surfaces. An interesting restriction! I try to find out whether the product of $x_i-x_j$ is a volume of some meaningful parallelepiped... | |
| Jun 24, 2010 at 12:56 | comment | added | Daniel Litt | Obviously I'm OK with some algebraic manipulation. That said, the type of proof I had in mind might be something like: take a rectangular prism containing the parallelepiped in question and subtract out the volume of some leftover simplices. Or find some other polytope with the same volume and prove synthetically that their volumes match. | |
| Jun 24, 2010 at 10:47 | comment | added | Wadim Zudilin | The question is really nice but it's probably hard to interpret purely geometrically the powers of $x_j$, the algebraic "addition" in Charles's argument seems to be unavoidable. It's probably a good reason to understand the product $\prod_{1\le i<j\le n}(x_i-x_j)$ from a geometric point of view. It's square, the discriminant, possesses some "hidden" geometry for small $n$ (in the theory of elliptic curves, for example) but probably not the product itself... | |
| Jun 24, 2010 at 5:34 | answer | added | Terry Tao | timeline score: 7 | |
| Jun 24, 2010 at 0:00 | answer | added | Pietro Majer | timeline score: 24 | |
| Jun 23, 2010 at 20:46 | history | edited | Charles Matthews | CC BY-SA 2.5 |
downcase
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| Jun 23, 2010 at 17:45 | history | edited | Daniel Litt | CC BY-SA 2.5 |
Sign error
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| Jun 23, 2010 at 17:06 | answer | added | Charles Siegel | timeline score: 14 | |
| Jun 23, 2010 at 16:01 | history | asked | Daniel Litt | CC BY-SA 2.5 |