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

Troy Lee, Dirk Oliver Theis
2013 arXiv   pre-print
The positive semidefinite rank of a nonnegative (m× n)-matrix S is the minimum number q such that there exist positive semidefinite (q× q)-matrices A_1,...,A_m, B_1,...,B_n such that S(k,ℓ) = tr(A_k^* B_ℓ). 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.
arXiv:1203.3961v4 fatcat:xmzv2c6gafbazc2anuk63xm2wm