Timeline for How many minors I need to check to conclude all minors will vanish ?
Current License: CC BY-SA 2.5
17 events
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| Nov 1, 2010 at 15:00 | comment | added | Vagabond | @Steven Sam I was curious about generalized vandermonde matrices whose determinants vanishes. As I was surfing through the literature quite at random I came across some argument in a paper which goes like this: its a $3x4$ matrix with rows $({a_{i}}^{j_k}- s^{j_k})(i=1,2,3),j=1,..,4$. Then it says note for all minors to vanish, it is enough to show that two of them vanish. See page 17 of this paper Tropical secant graphs of monomial curves arxiv.org/pdf/1005.3364 | |
| Oct 29, 2010 at 13:30 | comment | added | Steven Sam | @Vagabond: You seem to be unsatisfied with the question you asked (or at least the answers you received). Could you explain exactly what you are trying to do? I think the bottomline is this: even with the Plücker relations, given any fixed set of minors, you can't deduce anything about the other minors in general (for example for a given matrix your minors could be 0 and that tells you nothing about the others). Of course you can in certain cases, so if you have more information about the matrix that certainly changes the problem. | |
| Oct 29, 2010 at 7:32 | history | edited | Vagabond | CC BY-SA 2.5 |
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| Oct 28, 2010 at 19:12 | vote | accept | Vagabond | ||
| Oct 28, 2010 at 19:11 | vote | accept | Vagabond | ||
| Oct 28, 2010 at 19:11 | |||||
| Oct 28, 2010 at 16:28 | comment | added | Cam McLeman | @Sheik: That wasn't intended as a criticism, more a prod to refine the question. | |
| Oct 28, 2010 at 15:48 | comment | added | Sheikraisinrollbank | You guys are being somewhat too hard on Vagabond. I'm suprised nobody mentioned Plucker relations right away; they'll obviously help him/her understand. | |
| Oct 28, 2010 at 15:41 | answer | added | Sheikraisinrollbank | timeline score: 12 | |
| Oct 28, 2010 at 13:56 | answer | added | Steven Sam | timeline score: 19 | |
| Oct 28, 2010 at 13:28 | answer | added | Jørgen Rennemo | timeline score: 5 | |
| Oct 28, 2010 at 13:27 | comment | added | Tom Goodwillie | What? No, that worst case is always there to deal with. Take an mxm identity matrix and fill in the rest of the mxn matrix with zeroes. | |
| Oct 28, 2010 at 13:01 | comment | added | Vagabond | I know that's kind of a worst case scenario. I am hoping when $m$ and $n$ are comparable, for example when $n=m+1$ or $m+2$ one can do much better. I feel there is a lot of redundancy in these cases. | |
| Oct 28, 2010 at 12:53 | comment | added | Cam McLeman | Take a $2\times n$ matrix $A$ with all entries 0 except $A_{1,1}=A_{2,n}=1$. | |
| Oct 28, 2010 at 12:51 | history | edited | Vagabond |
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| Oct 28, 2010 at 12:46 | answer | added | Thierry Zell | timeline score: 1 | |
| Oct 28, 2010 at 12:39 | history | edited | Vagabond |
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| Oct 28, 2010 at 12:06 | history | asked | Vagabond | CC BY-SA 2.5 |