Timeline for "Circulant-Vandermonde" matrix: in search of a formula
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2022 at 23:19 | comment | added | paul garrett | If I were tasked with understanding this, I'd use the UFD-ness of $\mathbb Z[x_1,\ldots,x_n]$ and/or $\mathbb C[x_1,\ldots,x_n]$, and make adroit choices of values of the $x$'s to get vanishing, ... much as we do for Vandermonde. | |
| Jul 16, 2022 at 21:29 | history | edited | LSpice | CC BY-SA 4.0 |
`\eqref`, and `\cdots` and `\ddots` in matrices
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| Jul 16, 2022 at 21:14 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
edited title
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| Jul 16, 2022 at 19:49 | comment | added | Wolfgang | Sure that these are beautiful cyclic patterns. But if even for $n=3$, the determinant doesn't seem to allow any kind of decomposition and the discriminant is as it is, there won't be a lot of hope. Unless you can find "nice" eigenvectors, but even for e.g. $(x_1,x_2,x_3)=(1,2,4)$ there is nothing nice... :( | |
| Jul 16, 2022 at 17:09 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
added 20 characters in body
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| Jul 16, 2022 at 17:07 | comment | added | user61318 | Not sure what one can say from three examples. What do you mean by more experimentation? What did it reveal? Do you expect a nice answer merely because of the circulant case? In fact, why stop at the Vandermonde determinant. Take alternants with exponents of the form $\lambda_i+n-i$. | |
| Jul 16, 2022 at 16:38 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
edited title
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| Jul 16, 2022 at 15:28 | history | asked | T. Amdeberhan | CC BY-SA 4.0 |