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A Trace Bound For Integer-Diagonal Positive Semidefinite Matrices, Lon Mitchell
A Trace Bound For Integer-Diagonal Positive Semidefinite Matrices, Lon Mitchell
USF St. Petersburg campus Faculty Publications
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.