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arXiv:2310.16567 · Journal of Physics A Mathematical and Theoretical

Inertia of partial transpose of positive semidefinite matrices

Yixuan Liang, Jiahao Yan, Dongran Si, Lin Chen

Published Mar 5, 2024• 5 citations
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Abstract

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.

DOI
10.1088/1751-8121/ad3056

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