Inertia of partial transpose of positive semidefinite matrices
Quantum Physics
2023-10-26 v1
Abstract
We show that the partial transpose of 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 positive semidefinite matrices.
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