Simultaneous kernels of matrix Hadamard powers
Rings and Algebras
2019-05-17 v3
Abstract
In previous work [Adv. Math. 298, pp. 325-368, 2016], the structure of the simultaneous kernels of Hadamard powers of any positive semidefinite matrix were described. Key ingredients in the proof included a novel stratification of the cone of positive semidefinite matrices and a well-known theorem of Hershkowitz, Neumann, and Schneider, which classifies the Hermitian positive semidefinite matrices whose entries are or in modulus. In this paper, we show that each of these results extends to a larger class of matrices which we term -PMP (principal minor positive).
Cite
@article{arxiv.1709.03280,
title = {Simultaneous kernels of matrix Hadamard powers},
author = {Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar},
journal= {arXiv preprint arXiv:1709.03280},
year = {2019}
}
Comments
12 pages. Final version, to appear in Linear Algebra and its Applications (the journal version is longer)