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arXiv · 1709.03280

Simultaneous kernels of matrix Hadamard powers

Alexander Belton·Dominique Guillot·Apoorva Khare·Mihai Putinar
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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 $0$ 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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Alexander Belton, Dominique Guillot, Apoorva Khare, Mihai Putinar. 2017-09-11. Simultaneous kernels of matrix Hadamard powers. https://doi.org/10.1016/j.laa.2018.03.035

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