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    Rights statement: 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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Simultaneous kernels of matrix Hadamard powers

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Simultaneous kernels of matrix Hadamard powers. / Belton, Alexander; Guillot, Dominique; Khare, Apoorva et al.
In: Linear Algebra and its Applications, Vol. 576, 01.09.2019, p. 142-157.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Belton, A, Guillot, D, Khare, A & Putinar, M 2019, 'Simultaneous kernels of matrix Hadamard powers', Linear Algebra and its Applications, vol. 576, pp. 142-157. https://doi.org/10.1016/j.laa.2018.03.035

APA

Belton, A., Guillot, D., Khare, A., & Putinar, M. (2019). Simultaneous kernels of matrix Hadamard powers. Linear Algebra and its Applications, 576, 142-157. https://doi.org/10.1016/j.laa.2018.03.035

Vancouver

Belton A, Guillot D, Khare A, Putinar M. Simultaneous kernels of matrix Hadamard powers. Linear Algebra and its Applications. 2019 Sept 1;576:142-157. Epub 2018 Mar 20. doi: 10.1016/j.laa.2018.03.035

Author

Belton, Alexander ; Guillot, Dominique ; Khare, Apoorva et al. / Simultaneous kernels of matrix Hadamard powers. In: Linear Algebra and its Applications. 2019 ; Vol. 576. pp. 142-157.

Bibtex

@article{a1f894b106894301870365f0f52faf50,
title = "Simultaneous kernels of matrix Hadamard powers",
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).",
keywords = "Positive semidefinite matrix, Hadamard product, Schubert cell-type stratification, principal minor positive, principal submatrix rank property, simultaneous kernel",
author = "Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar",
note = "This is the author{\textquoteright}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",
year = "2019",
month = sep,
day = "1",
doi = "10.1016/j.laa.2018.03.035",
language = "English",
volume = "576",
pages = "142--157",
journal = "Linear Algebra and its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",

}

RIS

TY - JOUR

T1 - Simultaneous kernels of matrix Hadamard powers

AU - Belton, Alexander

AU - Guillot, Dominique

AU - Khare, Apoorva

AU - Putinar, Mihai

N1 - 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

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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).

AB - 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).

KW - Positive semidefinite matrix

KW - Hadamard product

KW - Schubert cell-type stratification

KW - principal minor positive

KW - principal submatrix rank property

KW - simultaneous kernel

U2 - 10.1016/j.laa.2018.03.035

DO - 10.1016/j.laa.2018.03.035

M3 - Journal article

VL - 576

SP - 142

EP - 157

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -