S-semigoodness for Low-Rank Semidefinite Matrix Recovery
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We extend and characterize the concept of s-semigoodness for a sensing matrix in sparse nonnegative recovery (proposed by Juditsky , Karzan and Nemirovski [Math Program, 2011]) to the linear transformations in low-rank semidefinite matrix recovery. We show that ssemigoodnessis not only a necessary and sufficient condition for exact s-rank semidefinitematrix recovery by a semidefinite program, but also provides a stable recovery under someconditions. We also show that both s-semigoodness and semiNSP are equivalent.
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