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Minimum of $\mathrm{rank}\left( \boldsymbol{W} \boldsymbol{H} \right)$, with $\boldsymbol{W}$ block diagonal
Let us assume that we have a full-rank $(n\cdot l)\times k$ matrix, $\boldsymbol{H}$, with no specific structure (e.g., a realization of a Gaussian i.i.d. random matrix), and an $m\times (n\cdot l)$ ...
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