Timeline for Invertibility of a matrix whose entries are certain binomial coefficients
Current License: CC BY-SA 3.0
11 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Feb 25, 2015 at 23:58 | vote | accept | Liliam | ||
Feb 21, 2015 at 18:52 | comment | added | Alex Degtyarev | @JasonStarr: thanks, this is nice. For proof, I guess, this is the interpolation by Newton "monomials" rather than conventional ones, right? | |
Feb 21, 2015 at 17:53 | comment | added | Jason Starr | @AlexDegtyarev. For elements $a_0,\dots,a_{n-1}$ in a commutative ring $R$, the Vandermonde determinant $\text{det}(a_i^j)_{0\leq i,j\leq n-1}$ equals $0!\cdot 1!\cdots (n-1)!$ times the determinant $\text{det}(\binom{a_i}{j})_{0\leq i,j\leq n-1}$. Thus, the determinant above is, up to a product of factorials, a Vandermonde determinant. | |
Feb 21, 2015 at 17:01 | answer | added | Chris McDaniel | timeline score: 6 | |
Feb 21, 2015 at 17:01 | review | Close votes | |||
Feb 21, 2015 at 17:43 | |||||
Feb 21, 2015 at 16:59 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Tried to improve the formulation of the question.
|
Feb 21, 2015 at 16:50 | comment | added | Alex Degtyarev | @JasonStarr How do you reduce this to Vandermonde? Just curious :) | |
Feb 21, 2015 at 16:40 | comment | added | Liliam | Yes, but Vandermonde determinant didn't solve the problem. I found a paper that solves the problem but to a much more general case. I would like a more simpler solution, I believe it exists. | |
Feb 21, 2015 at 16:33 | review | First posts | |||
Feb 21, 2015 at 16:50 | |||||
Feb 21, 2015 at 16:32 | comment | added | Jason Starr | Have you searched for "Vandermonde determinant"? | |
Feb 21, 2015 at 16:30 | history | asked | Liliam | CC BY-SA 3.0 |