Timeline for PSD matrix with non-negative entries
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2011 at 6:24 | comment | added | Pawan Aurora | The fact that the above matrix is not Completely Positive tells us that for any $M>5$, we cannot find five vectors in the non-negative orthant of $R^{M}$ that have their mutual dot products given by the Gram matrix $A$ above. So for $M>5$ there obviously exist counter examples. | |
| Jun 9, 2011 at 17:44 | comment | added | Suvrit | @Denis: thanks for your comments; I will think about this a bit more when I get a chance. @Pawan: I guess so; perhaps merely embedding this 5 x 5 matrix as a principal submatrix of a larger matrix should do the trick---not sure. | |
| Jun 9, 2011 at 16:59 | comment | added | Pawan Aurora | Does this example in some way generalize to $M>5$? | |
| Jun 9, 2011 at 16:18 | comment | added | Denis Serre | Nevertheless, I made calculations which convince me that this matrix is a counter-example. | |
| Jun 9, 2011 at 15:30 | comment | added | Denis Serre | @Suvrit. That $A$ is not $X^TX$ for an $X$ with non-negative entries does not make a counter-example. | |
| Jun 9, 2011 at 13:09 | history | edited | Suvrit | CC BY-SA 3.0 |
added missing word
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| Jun 9, 2011 at 10:35 | history | answered | Suvrit | CC BY-SA 3.0 |