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 s-semigoodness is not only a necessary and sufficient condition for exact $s$-rank semidefinite matrix recovery by a semidefinite program, but also provides a stable recovery under some conditions. We also show that both s-semigoodness and semiNSP are equivalent.
Department of Applied Mathematics, Beijing Jiaotong University, Research Report, 2013
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