A 2n(2) - log(2)(n)-1 Lower Bound for the Border Rank of Matrix Multiplication

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A 2n(2) - log(2)(n)-1 Lower Bound for the Border Rank of Matrix Multiplication. / Landsberg, Joseph M.; Michalek, Mateusz.

In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES, No. 15, 08.2018, p. 4722-4733.

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Landsberg, Joseph M. ; Michalek, Mateusz. / A 2n(2) - log(2)(n)-1 Lower Bound for the Border Rank of Matrix Multiplication. In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. 2018 ; No. 15. pp. 4722-4733.

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@article{b6f2042831e14056882bd1c2f29844be,
title = "A 2n(2) - log(2)(n)-1 Lower Bound for the Border Rank of Matrix Multiplication",
abstract = "Let M- is an element of C-n2 circle times C-n2 circle times C-n2 denote the matrix multiplication tensor for n x n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings [8] to prove the border rank lower bound R(M-) >= 2n(2) - [log(2)(n)] - 1.",
author = "Landsberg, {Joseph M.} and Mateusz Michalek",
year = "2018",
month = "8",
doi = "10.1093/imrn/rnx025",
language = "English",
pages = "4722--4733",
journal = "INTERNATIONAL MATHEMATICS RESEARCH NOTICES",
issn = "1073-7928",
number = "15",

}

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TY - JOUR

T1 - A 2n(2) - log(2)(n)-1 Lower Bound for the Border Rank of Matrix Multiplication

AU - Landsberg, Joseph M.

AU - Michalek, Mateusz

PY - 2018/8

Y1 - 2018/8

N2 - Let M- is an element of C-n2 circle times C-n2 circle times C-n2 denote the matrix multiplication tensor for n x n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings [8] to prove the border rank lower bound R(M-) >= 2n(2) - [log(2)(n)] - 1.

AB - Let M- is an element of C-n2 circle times C-n2 circle times C-n2 denote the matrix multiplication tensor for n x n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings [8] to prove the border rank lower bound R(M-) >= 2n(2) - [log(2)(n)] - 1.

U2 - 10.1093/imrn/rnx025

DO - 10.1093/imrn/rnx025

M3 - Article

SP - 4722

EP - 4733

JO - INTERNATIONAL MATHEMATICS RESEARCH NOTICES

JF - INTERNATIONAL MATHEMATICS RESEARCH NOTICES

SN - 1073-7928

IS - 15

ER -

ID: 30273001