Timeline for Proving a determinant = 0
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2023 at 8:17 | comment | added | user178594 | Sorry, this post asks about two questions, so it needs more focus. | |
| Jan 15, 2013 at 4:29 | comment | added | Erick Wong | @wccanard I agree that (C), taken only as a sufficient condition for $\det A = 0$, doesn't need a name. But Frobenius-König also yields a partial converse, that any configuration of zeros which guarantees a zero determinant necessarily contains this form (at least when working over a large enough field). | |
| Jan 15, 2013 at 1:58 | history | edited | Curt Monash | CC BY-SA 3.0 |
added 8 characters in body
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| Jan 15, 2013 at 1:54 | comment | added | Curt Monash | Frobenius-Koenig looks like what I need. Thanks! | |
| Jan 15, 2013 at 1:47 | history | edited | Curt Monash | CC BY-SA 3.0 |
added 148 characters in body
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| Jan 14, 2013 at 10:29 | comment | added | Tom Smith | (B) is another way of saying "Find a (non-zero) vector in the null-space of the matrix". | |
| Jan 13, 2013 at 18:14 | answer | added | Zsbán Ambrus | timeline score: 1 | |
| Jan 13, 2013 at 16:06 | answer | added | Casteels | timeline score: 2 | |
| Jan 13, 2013 at 16:00 | answer | added | wh0 | timeline score: 1 | |
| Jan 13, 2013 at 12:06 | comment | added | user30035 | I'm not sure (C) deserves a name. It's a trivial consequence of the definition of a determinant as a sum over the symmetric group (and the pigeonhole principle, if you like): all $n!$ terms in the sum are zero. | |
| Jan 13, 2013 at 11:32 | comment | added | Felix Goldberg | @EricWong: Or, rather, the determinantal Frobenius-Konig theorem (the original deals with the permanent). | |
| Jan 13, 2013 at 11:02 | comment | added | Carlo Beenakker | how about calculating the determinant? it's an $O(N^3)$ operation, so any alternative would have to be more efficient | |
| Jan 13, 2013 at 9:09 | answer | added | Easy | timeline score: 0 | |
| Jan 13, 2013 at 8:47 | comment | added | Erick Wong | The answer to your minor question is the Frobenius-König theorem. | |
| Jan 13, 2013 at 8:45 | history | asked | Curt Monash | CC BY-SA 3.0 |