Timeline for Product $PVPVP$ is elementwise nonnegative?
Current License: CC BY-SA 3.0
24 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2016 at 13:26 | history | edited | vansy | CC BY-SA 3.0 |
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| Apr 7, 2016 at 22:49 | vote | accept | vansy | ||
| Apr 7, 2016 at 22:49 | vote | accept | vansy | ||
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| Apr 7, 2016 at 22:29 | vote | accept | vansy | ||
| Apr 7, 2016 at 22:49 | |||||
| Jan 10, 2016 at 6:34 | answer | added | Terry Tao | timeline score: 11 | |
| Dec 22, 2015 at 22:22 | comment | added | Fan Zheng | Is $P$ symmetric? Otherwise what do you mean by positive definiteness? | |
| Dec 11, 2015 at 2:38 | answer | added | Timothy Chow | timeline score: 2 | |
| S Oct 14, 2015 at 14:58 | history | suggested | Chris Ramsey | CC BY-SA 3.0 |
This is a reasonable question and I hope with the added simplification an answer to the original problem will be found.
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| Oct 14, 2015 at 14:36 | review | Suggested edits | |||
| S Oct 14, 2015 at 14:58 | |||||
| Oct 31, 2014 at 4:45 | comment | added | The Masked Avenger | Suppose you get lucky and find that the sum of the expressions is less than the expression of the sum, then you might be able to extend that to your desired inequality. If not, it might lead you to a counterexample. | |
| Oct 30, 2014 at 16:01 | comment | added | vansy | @TheMaskedAvenger: could you elaborate on it? | |
| Oct 29, 2014 at 19:26 | comment | added | The Masked Avenger | Let V be the zero matrix plus a nonzero element in row 1, column 1. Define W similarly, using 2 instead of 1. Let Y be V+W. Is there a helpful relation among PXPXP for X ranging over V, W, and Y? | |
| Oct 29, 2014 at 14:58 | history | edited | vansy | CC BY-SA 3.0 |
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| Oct 29, 2014 at 14:57 | comment | added | vansy | @JoonasIlmavirta: Thanks for your comments. Just edited the question. I'll be more careful next time. | |
| Oct 29, 2014 at 14:50 | history | edited | vansy | CC BY-SA 3.0 |
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| Oct 29, 2014 at 11:55 | comment | added | cardinal | @Suvrit: As usual, no slowness on your part whatsoever. Given the ever-so-slightly stilted statement of the question (and the crosspost from math.SE), I interpreted nonnegative to be positive semidefinite and so I provided a straightforward hint with that in mind. But, it now appears that was an incorrect inference. | |
| Oct 29, 2014 at 6:11 | comment | added | Joonas Ilmavirta | @mathnotgoodatmath, if you repost, it's polite to mention it and give a link. Therefore I added the comment. About the question itself: It could be a good idea to include the definition of nonnegativity in the question. I first thought the question was simple, but then I realised that nonnegativity must mean something other than positive semidefiniteness and had to find the definitions. | |
| Oct 29, 2014 at 5:28 | comment | added | vansy | @cardinal: could you please be more specific? The product is positive semi-definite. But it is not obvious to me that it is a non-negative matrix. Thanks. | |
| Oct 29, 2014 at 5:14 | comment | added | vansy | @JoonasIlmavirta: I posted the question at MSE but have not received any help since then, so I decided to re-post it here. | |
| Oct 29, 2014 at 5:02 | comment | added | Suvrit | @cardinal: please excuse my slowness, but is it then immediate that one gets elementwise nonnegativity? | |
| Oct 29, 2014 at 0:01 | comment | added | cardinal | Hint: There exists $S \in \mathbb R^{n \times n}$ such that $P = S^2 = S^T S$. Now, use the definition of nonnegative definiteness. | |
| Oct 28, 2014 at 20:29 | review | First posts | |||
| Oct 28, 2014 at 21:33 | |||||
| Oct 28, 2014 at 20:26 | comment | added | Joonas Ilmavirta | The same question was asked about a week ago at MSE: math.stackexchange.com/q/985073/166535 | |
| Oct 28, 2014 at 20:20 | history | asked | vansy | CC BY-SA 3.0 |