Simultaneous kernels of matrix Hadamard powers
Copyright policy )Simultaneous kernels of matrix Hadamard powers
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).
12 pages. Final version, to appear in Linear Algebra and its Applications (the journal version is longer)
- Lancaster University United Kingdom
- University of California Santa Barbara
- Indian Institute of Science Bangalore India
- University of California, Santa Barbara United States
- University of Delaware United States
Hadamard product, principal minor positive, Numerical & Computational Mathematics, principal submatrix rank property, 15B48 (Primary) 15A21 (Secondary), Mathematical Sciences, 510, Positive matrices and their generalizations; cones of matrices, Engineering, 15B48 (Primary) 15A21, Information and Computing Sciences, Principal minor positive, FOS: Mathematics, Schubert cell-type stratification, math.RA, Principal submatrix rank property, Vector spaces, linear dependence, rank, lineability, Simultaneous kernel, Mathematics - Rings and Algebras, 620, positive semidefinite matrix, Positive semidefinite matrix, Rings and Algebras (math.RA), Others
Hadamard product, principal minor positive, Numerical & Computational Mathematics, principal submatrix rank property, 15B48 (Primary) 15A21 (Secondary), Mathematical Sciences, 510, Positive matrices and their generalizations; cones of matrices, Engineering, 15B48 (Primary) 15A21, Information and Computing Sciences, Principal minor positive, FOS: Mathematics, Schubert cell-type stratification, math.RA, Principal submatrix rank property, Vector spaces, linear dependence, rank, lineability, Simultaneous kernel, Mathematics - Rings and Algebras, 620, positive semidefinite matrix, Positive semidefinite matrix, Rings and Algebras (math.RA), Others
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