Timeline for How many minors I need to check to conclude all minors will vanish ?
Current License: CC BY-SA 2.5
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| Oct 28, 2010 at 13:44 | comment | added | Thierry Zell | Ooops! What I wrote works best for matrices whose entries are variables (as in the determinantal varieties case), but of course, as Jorgen's example points out, it does not work so well with matrices that have a lot of zero entries (you cannot get much out of the expansion along your new row if your last minor is multiplied by zero!). | |
| Oct 28, 2010 at 13:41 | comment | added | Steven Sam | And what if one of the columns of the $m \times (m+1)$ matrix is all 0's? Your method of obtaining a relation would fail because it would like like $0=0$. In fact, this is precisely a scenario where you need to check all minors (because all but one possibly vanish) Any answer that suggests that you don't need to check all of the minors will be wrong. | |
| Oct 28, 2010 at 12:46 | history | answered | Thierry Zell | CC BY-SA 2.5 |