# Ziv Goldfeld

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 Name Ziv Goldfeld Member for 6 months Seen Feb 14 at 10:09 Website Location Age
 Jan20 comment Convexity of a Certain Set of Covariance MatricesI'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! Jan19 asked Convexity of a Certain Set of Covariance Matrices Jan5 comment Schur complement and negative definite matricesThank you. By the way, why is it important to have $C>0$ (or $C<0$ for the negative version) in order to use the lemma? Why isn't $C\neq 0$ enough? I ask it since we do not demand anything regarding the matrices $A$ and $B$ as far as non-negativeness, but we do demand it for $C$. Why is that? Jan4 comment Schur complement and negative definite matricesOhh I'm sorry, I accidentally mixed the two version of the lemma. I've edited the original question and now I think it's fine; thanks for the remark! So you say that $M\leq 0$ iff $C<0$ and $A-BC^{-1}B^T$ holds? Any ideas regarding the second question? Thanks again! Jan4 revised Schur complement and negative definite matricesdeleted 13 characters in body Jan4 revised Schur complement and negative definite matricesadded 22 characters in body; deleted 5 characters in body; added 8 characters in body Jan4 awarded ● Editor Jan4 revised Schur complement and negative definite matricesadded 552 characters in body Jan4 asked Schur complement and negative definite matrices