Timeline for Size of a minimal non-negative conic basis
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 18, 2018 at 18:43 | vote | accept | Rajesh Jayaram | ||
| May 18, 2018 at 18:43 | comment | added | Rajesh Jayaram | Right, I found it suspect to begin with. I managed to find a counter-example to my last question, which shows that even for k=3 we can pick arbitrarily many non-negative vectors such that none is a conic combination of the others. For instance, one can take arbitrarily many distinct vectors on the boundary of a circular cone contained in the positive orthant. | |
| May 17, 2018 at 13:01 | comment | added | Tony Huynh | Indeed, that claim in the wikipedia article appears to be fallacious. | |
| May 16, 2018 at 11:41 | comment | added | Rajesh Jayaram | Thanks! It seems that this conflicts with the statement: "The non-negative rank is in general strictly greater than the largest number of columns such that no selected column can be written as a nonnegative linear combination of the other selected columns." (en.wikipedia.org/wiki/…). Perhaps strict inequality is not meant here (since 3 is the largest such number in your example). I am wondering now whether any bound can be given in terms of k? For instance, is 4 an upper bound for the case of k=3, or can rank_+^*(V) be arbitrarily large? | |
| May 16, 2018 at 1:37 | history | edited | Tony Huynh | CC BY-SA 4.0 |
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| May 16, 2018 at 1:26 | history | edited | Tony Huynh | CC BY-SA 4.0 |
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| May 16, 2018 at 0:53 | history | edited | Tony Huynh | CC BY-SA 4.0 |
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| May 16, 2018 at 0:23 | history | answered | Tony Huynh | CC BY-SA 4.0 |