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Let $X,Y\in\mathbb{R}^{n\times n}$ be symmetric matrices. You may assume that $X$ is positive semidefinite and $Y$ negative semidefinite, if needed, but not that they are invertible. I would like to ...

I came across this question and got really interested about it. There, the OP asks whether is possible to decompose a $2n \times 2n$ block matrix: $$ \begin{pmatrix} X & I \\ I & Y \end{...