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Belton, Alexander; Guillot, Dominique; Khare, Apoorva; Putinar, Mihai
Linear algebra and its applications, 09/2019, Volume: 576Journal Article
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).
