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Abstract We show that the partial transpose of 9 × 9 positive semidefinite matrices do not have inertia ( 4 , 1 , 4 ) and ( 3 , 2 , 4 ) . It solves an open problem in ‘LINEAR AND MULTILINEAR ALGEBRA. Changchun Feng et al , 2022’. We apply our results to construct some inertia, as well as present the list of all possible inertia of partial transpose of 12 × 12 positive semidefinite matrices.
Liang et al. (Tue,) studied this question.