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This question is about the positive definiteness of a (non-random) matrix that is defined using random variables as follows: We fix the vector $v=(1,1)$ (yet, it seems the final result does not ...

We consider block matrices $$\mathcal A = \begin{pmatrix} 0 & A\\A^* & 0 \end{pmatrix}$$ and $$\mathcal B = \begin{pmatrix} 0 & B\\C & 0 \end{pmatrix}.$$ Then we define the new matrix $...