A 2n2-log2(n)-1 lower bound for the border rank of matrix multiplication
| dc.contributor.author | Landsberg, Joseph M. | |
| dc.contributor.author | Michalek, Mateusz | |
| dc.date.accessioned | 2021-03-23T09:44:04Z | |
| dc.date.available | 2021-03-23T09:44:04Z | |
| dc.date.issued | 2018 | eng |
| dc.description.abstract | Let M⟨n⟩ ∈ Cn2⊗Cn2⊗Cn2 denote the matrix multiplication tensor for n×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⟨n,n,n⟩)≥2n2−⌈log2(n)⌉−1. | eng |
| dc.description.version | published | eng |
| dc.identifier.doi | 10.1093/imrn/rnx025 | eng |
| dc.identifier.uri | https://kops.uni-konstanz.de/handle/123456789/53233 | |
| dc.language.iso | eng | eng |
| dc.rights | terms-of-use | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| dc.subject.ddc | 510 | eng |
| dc.title | A 2n<sup>2</sup>-log<sub>2</sub>(n)-1 lower bound for the border rank of matrix multiplication | eng |
| dc.type | JOURNAL_ARTICLE | eng |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @article{Landsberg2018lower-53233,
year={2018},
doi={10.1093/imrn/rnx025},
title={A 2n<sup>2</sup>-log<sub>2</sub>(n)-1 lower bound for the border rank of matrix multiplication},
number={15},
volume={2018},
issn={1073-7928},
journal={International Mathematics Research Notices},
pages={4722--4733},
author={Landsberg, Joseph M. and Michalek, Mateusz}
} | |
| kops.citation.iso690 | LANDSBERG, Joseph M., Mateusz MICHALEK, 2018. A 2n2-log2(n)-1 lower bound for the border rank of matrix multiplication. In: International Mathematics Research Notices. Oxford University Press (OUP). 2018, 2018(15), pp. 4722-4733. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnx025 | deu |
| kops.citation.iso690 | LANDSBERG, Joseph M., Mateusz MICHALEK, 2018. A 2n2-log2(n)-1 lower bound for the border rank of matrix multiplication. In: International Mathematics Research Notices. Oxford University Press (OUP). 2018, 2018(15), pp. 4722-4733. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnx025 | eng |
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<dcterms:abstract xml:lang="eng">Let M<sub>⟨n⟩</sub> ∈ C<sup>n2</sup>⊗C<sup>n2</sup>⊗C<sup>n2</sup> denote the matrix multiplication tensor for n×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<sub>⟨n,n,n⟩</sub>)≥2n<sup>2</sup>−⌈log<sub>2</sub>(n)⌉−1.</dcterms:abstract>
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| kops.sourcefield | International Mathematics Research Notices. Oxford University Press (OUP). 2018, <b>2018</b>(15), pp. 4722-4733. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnx025 | deu |
| kops.sourcefield.plain | International Mathematics Research Notices. Oxford University Press (OUP). 2018, 2018(15), pp. 4722-4733. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnx025 | deu |
| kops.sourcefield.plain | International Mathematics Research Notices. Oxford University Press (OUP). 2018, 2018(15), pp. 4722-4733. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnx025 | eng |
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| source.identifier.eissn | 1687-0247 | eng |
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| source.publisher | Oxford University Press (OUP) | eng |