Timeline for Convexity of a Certain Set of Covariance Matrices
Current License: CC BY-SA 3.0
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| Jan 20, 2013 at 10:03 | comment | added | AD1984 | I'm sorry, but I didn't understand your answer fully. When you say that the data are independent apart from some inequalities do you mean the following: $\Sigma_i-\Sigma_{iU}\Sigma_U^{-1}\Sigma_{Ui}\geq 0$, and the non-negativety constraints, i.e., $\Sigma_i\geq 0$ and $\Sigma_U\geq 0$, where $i=1,2$. Are there any additional relations between the data matrices? What do you mean by "leaves room for an open set"? And finally, why $A$ must be linear if the set is to be convex? There are convex sets that are not linear. I'd appreciate if you could clarify this for me. Thank you in advance! | |
| Jan 19, 2013 at 22:24 | comment | added | Denis Serre | Obviously not. The data $\Sigma_{U,1,2,1U, U2}$ are independent apart from inequalities that leaves room for an open set. If the set was convex, $A$ would be a linear function of these data, but it is not. A natural question is: what is the convex hull of the set of such matrices? | |
| Jan 19, 2013 at 17:59 | history | asked | AD1984 | CC BY-SA 3.0 |