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For questions involving the trace of a square matrix, i.e. the sum of the elements on the main diagonal.

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Submodularity property of trace of inverse matrix

$\newcommand{\tr}{\operatorname{tr}}$Does submodularity property hold for the trace of a positive-definite hermitian matrix? I.e., does given any real symmetric positive-definite matrices $X,A,B$ $$ …
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