Inequalities for permanents of Hermitian matrices (Q1368761)

Consider two Hermitian matrices which can be written in block form as: \[ A = \left(\begin{matrix} A_{1}&C\\ C*&A_{2}\end{matrix}\right) \quad \text{ and }\quad B = \left(\begin{matrix} B_{1}&C \\ C*&B_{2}\end{matrix}\right). \] The author proves: if \(A_{i}\), \(B_{i}\) and \(A_{i}-B_{i}\) (\(i = 1,2\)) are nonnegative semidefinite, then the permanents satisfy \(\text{per}(A) \geq \text{per}(B) \geq 0\).