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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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).

Item Type:

Journal Article

Journal or Publication Title:

Linear Algebra and its Applications

Additional Information:

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

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2607

Subjects:

?? positive semidefinite matrixhadamard productschubert cell-type stratificationprincipal minor positiveprincipal submatrix rank propertysimultaneous kerneldiscrete mathematics and combinatoricsalgebra and number theorygeometry and topologynumerical analysis ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

124099

Deposited By:

ep_importer_pure

Deposited On:

19 Mar 2018 09:20

Refereed?:

Yes

Published?:

Published

Last Modified:

02 Oct 2024 00:11

URI:

https://eprints.lancs.ac.uk/id/eprint/124099