We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r-1.
Mitchell, L. (2020). A trace bound for integer-diagonal positive semidefinite matrices. Special Matrices, 8(1), 14–16. https://doi.org/10.1515/spma-2020-0002
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