Simultaneous kernels of matrix Hadamard powers

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2019) Simultaneous kernels of matrix Hadamard powers. Linear Algebra and its Applications, 576. pp. 142-157. ISSN 0024-3795

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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).

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Journal Article
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Linear Algebra and its Applications
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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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19 Mar 2018 09:20
Last Modified:
09 Aug 2022 00:13