Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank

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Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank. / Gesmundo, Fulvio; Oneto, Alessandro; Ventura, Emanuele.

I: SIAM Journal on Matrix Analysis and Applications, Bind 40, Nr. 4, 2019, s. 1453-1477.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Gesmundo, F, Oneto, A & Ventura, E 2019, 'Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank', SIAM Journal on Matrix Analysis and Applications, bind 40, nr. 4, s. 1453-1477. https://doi.org/10.1137/18M1225422

APA

Gesmundo, F., Oneto, A., & Ventura, E. (2019). Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank. SIAM Journal on Matrix Analysis and Applications, 40(4), 1453-1477. https://doi.org/10.1137/18M1225422

Vancouver

Gesmundo F, Oneto A, Ventura E. Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank. SIAM Journal on Matrix Analysis and Applications. 2019;40(4):1453-1477. https://doi.org/10.1137/18M1225422

Author

Gesmundo, Fulvio ; Oneto, Alessandro ; Ventura, Emanuele. / Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank. I: SIAM Journal on Matrix Analysis and Applications. 2019 ; Bind 40, Nr. 4. s. 1453-1477.

Bibtex

@article{8f8c5b5dc7304b4096e46f2b6025e446,
title = "Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank",
abstract = "A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such as apolarity theory, we show how the study of the simultaneous symmetric rank of partial derivatives of the homogeneous polynomial associated to the symmetric tensor can be used to prove equalities among different partially symmetric ranks. This approach aims to understand to what extent the symmetries of a tensor affect its rank. We apply this to the special cases of binary forms, ternary and quaternary cubics, monomials, and elementary symmetric polynomials.",
author = "Fulvio Gesmundo and Alessandro Oneto and Emanuele Ventura",
year = "2019",
doi = "10.1137/18M1225422",
language = "English",
volume = "40",
pages = "1453--1477",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics",
number = "4",

}

RIS

TY - JOUR

T1 - Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank

AU - Gesmundo, Fulvio

AU - Oneto, Alessandro

AU - Ventura, Emanuele

PY - 2019

Y1 - 2019

N2 - A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such as apolarity theory, we show how the study of the simultaneous symmetric rank of partial derivatives of the homogeneous polynomial associated to the symmetric tensor can be used to prove equalities among different partially symmetric ranks. This approach aims to understand to what extent the symmetries of a tensor affect its rank. We apply this to the special cases of binary forms, ternary and quaternary cubics, monomials, and elementary symmetric polynomials.

AB - A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such as apolarity theory, we show how the study of the simultaneous symmetric rank of partial derivatives of the homogeneous polynomial associated to the symmetric tensor can be used to prove equalities among different partially symmetric ranks. This approach aims to understand to what extent the symmetries of a tensor affect its rank. We apply this to the special cases of binary forms, ternary and quaternary cubics, monomials, and elementary symmetric polynomials.

U2 - 10.1137/18M1225422

DO - 10.1137/18M1225422

M3 - Journal article

VL - 40

SP - 1453

EP - 1477

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 4

ER -

ID: 231712717