Simultaneous kernels of matrix Hadamard powers

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2019) Simultaneous kernels of matrix Hadamard powers. In: LINEAR ALGEBRA AND ITS APPLICATIONS, 576 . pp. 142-157.

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Abstract

In previous work Belton et al. (2016) 2], 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). (C) 2018 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	LINEAR ALGEBRA AND ITS APPLICATIONS
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	21st Conference of the International-Linear-Algebra-Society (ILAS), Iowa State Univ, Ames, IA, JUL 24-28, 2017 The copyright for this article belongs to Elsevier Inc.
Keywords:	Positive semidefinite matrix; Hadamard product; Schubert cell-type stratification; Principal minor positive; Principal submatrix rank property; Simultaneous kernel
Department/Centre:	Others
Date Deposited:	28 Jun 2019 06:38
Last Modified:	28 Jun 2019 06:38
URI:	http://eprints.iisc.ac.in/id/eprint/63104

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