A trace bound for integer-diagonal positive semidefinite matrices

Abstract

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.

Keywords

• positive semidefinite matrices
• integer-diagonal
• trace
• 15b48
• 15a15
• 05c50