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\end{eqnarray}  At the extremum, the matrix of the Lagrange multiplyers must be Hermitian, i.e.   \begin{eqnarray}  \lambda_{ki}-\lambda_{ik}^{*}=0\label{lambdaeq} \lambda_{ki}-\lambda_{ik}^{*}=0\label{eqlambda}  \end{eqnarray}  Then one can define the off diagonal elements of a Hermitian matrix $\mathbf{F}$ as:  \begin{eqnarray}