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Simultaneous kernels of matrix Hadamard powers

Lookup NU author(s): Professor Mihai Putinar



This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


In previous work [Adv.Math. 298:325-368, 2016], the structure of the simultaneous kernels of Hadamard powers of any positive semidefinite matrix was 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 0 or 1 in modulus. In this paper, we show that each of these results extends to a larger class of matrices which we term 3-PMP (principal minor positive).

Publication metadata

Author(s): Belton A, Guillot D, Khare A, Putinar M

Publication type: Article

Publication status: Published

Journal: Linear Algebra and its Applications

Year: 2018

Volume: 576

Pages: 142-157

Print publication date: 01/09/2019

Online publication date: 20/03/2018

Acceptance date: 17/03/2018

Date deposited: 14/06/2018

ISSN (print): 0024-3795

ISSN (electronic): 1873-1856

Publisher: Elsevier Inc.


DOI: 10.1016/j.laa.2018.03.035


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