English

Inertia of partial transpose of positive semidefinite matrices

Quantum Physics 2023-10-26 v1

Abstract

We show that the partial transpose of 9×99\times 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 12×1212\times 12 positive semidefinite matrices.

Keywords

Cite

@article{arxiv.2310.16567,
  title  = {Inertia of partial transpose of positive semidefinite matrices},
  author = {Yixuan Liang and Jiahao Yan and Dongran Si and Lin Chen},
  journal= {arXiv preprint arXiv:2310.16567},
  year   = {2023}
}

Comments

20 pages, comments are welcome