Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix
نویسندگان
چکیده
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 A1, . . . , Am, B1, . . . , Bn such that S(k, l) = trA∗kBl. The most important lower bound technique on nonnegative rank only uses the zero/nonzero pattern of the matrix. We characterize the power of lower bounds on positive semidefinite rank based on the zero/non-zero pattern.
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