Ziv Goldfeld
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Registered User
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Jan 20 |
comment |
Convexity of a Certain Set of Covariance Matrices 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! |
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Jan 19 |
asked | Convexity of a Certain Set of Covariance Matrices |
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Jan 5 |
comment |
Schur complement and negative definite matrices Thank 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? |
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Jan 4 |
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Schur complement and negative definite matrices Ohh 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! |
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Jan 4 |
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Schur complement and negative definite matrices deleted 13 characters in body |
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Jan 4 |
revised |
Schur complement and negative definite matrices added 22 characters in body; deleted 5 characters in body; added 8 characters in body |
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Jan 4 |
awarded | ● Editor |
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Jan 4 |
revised |
Schur complement and negative definite matrices added 552 characters in body |
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Jan 4 |
asked | Schur complement and negative definite matrices |
