Inertia of partial transpose of positive semidefinite matrices

Inertia of partial transpose of positive semidefinite matrices

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...

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Veröffentlicht in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2024-03, Vol.57 (12), p.125203
Hauptverfasser: Liang, Yixuan, Yan, Jiahao, Si, Dongran, Chen, Lin
Format: Artikel
Sprache:eng
Schlagworte:
inertia
non-positive-partial-transpose
NPT
positive semidefinite matrix
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Zusammenfassung: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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ad3056