Timeline for Finding a "special" non singular submatrix
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2015 at 14:59 | comment | added | Surb | Ok sorry, I misread your question. Also I did not notice that you require $I\cap J= \emptyset$ | |
| May 28, 2015 at 14:57 | comment | added | teide4 | First, I consider $I$ and $J$ as the rows and columns that do appear in $A_{I,J}$. Thus, the maximal sets in your example are the empty ones. | |
| May 27, 2015 at 22:34 | comment | added | Surb | It seems unlikely that such sets $I,J$ even exists for any matrix $A\in M_n(\Bbb Z)$. Define $A_{i,j}=2$ for every $i,j\in\{1,\ldots,n\}$. Then every sub-matrix $A_{I,J}$ is singular (and so $\det(A_{I,J})=0$) except when $|I|=|J|=n-1$, in which case $\det(A_{I,J})=\det(2)=2$... (and I did not mentioned the zero matrix...) | |
| May 27, 2015 at 10:24 | history | asked | teide4 | CC BY-SA 3.0 |