Linear inequalities for density matrices: IV Factorizations

Diagonal linear inequalities for variable-N ensembles were reported by McRae in his thesis involving up to seven orbitals simultaneously. Many of these were reported in a simple factored form. Starting with inequalities involving six orbitals there were several which could not be factored. Here we report a general method for writing any inequality of this type as a linear combination of average values of squares of operators.