Inertia of partial transpose of positive semidefinite matrices

2023/10/25 by Yixuan Liang, Liang, Yixuan, Jiahao Yan +5 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2310.16567

openalex publication_date 2023/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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