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    Rights statement: This is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, 576, 2019 DOI: 10.1016/j.laa.2018.03.035

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Simultaneous kernels of matrix Hadamard powers

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<mark>Journal publication date</mark>1/09/2019
<mark>Journal</mark>Linear Algebra and its Applications
Volume576
Number of pages16
Pages (from-to)142-157
Publication StatusPublished
Early online date20/03/18
<mark>Original language</mark>English

Abstract

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).

Bibliographic note

This is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, 576, 2019 DOI: 10.1016/j.laa.2018.03.035