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arXiv · 1203.3961

Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix

Troy Lee·Dirk Oliver Theis
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Abstract

The positive semidefinite rank of a nonnegative $(m\times n)$-matrix~$S$ is the minimum number~$q$ such that there exist positive semidefinite $(q\times q)$-matrices $A_1,\dots,A_m$, $B_1,\dots,B_n$ such that $S(k,\ell) = \mbox{tr}(A_k^* B_\ell)$. The most important, lower bound technique for nonnegative rank is solely based on the support of the matrix S, i.e., its zero/non-zero pattern. In this paper, we characterize the power of lower bounds on positive semidefinite rank based on solely on the support.

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Troy Lee, Dirk Oliver Theis. 2013-11-15. Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix. https://arxiv.org/abs/1203.3961

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