The positive semidefinite rank of a nonnegative (mΓn)-matrix~S is
the minimum number~q such that there exist positive semidefinite (qΓq)-matrices A1β,β¦,Amβ, B1β,β¦,Bnβ 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.Comment: 9 page