Partial Degeneration of Tensors

DOI10.1137/23m1554898arXiv2212.14095OpenAlexW4392650278MaRDI QIDQ6130652

Unnamed Author, Vladimir Lysikov, Fulvio Gesmundo, Matthias Christandl

Publication date: 3 April 2024

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.14095

zbMATH Keywords

degenerationrestrictiontensor rank

Mathematics Subject Classification ID

Multilinear algebra, tensor calculus (15A69) Complexity classes (hierarchies, relations among complexity classes, etc.) (68Q15) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Secant varieties, tensor rank, varieties of sums of powers (14N07)

Cites Work

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• \(0(n^{2.7799})\) complexity for \(n\times n\) approximate matrix multiplication
• Tensor rank is not multiplicative under the tensor product
• Rank and border rank of Kronecker powers of tensors and Strassen's laser method
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• Bounds on complexity of matrix multiplication away from Coppersmith-Winograd tensors
• Relative bilinear complexity and matrix multiplication.
• Optimal Evaluation of Pairs of Bilinear Forms
• A classification of irreducible prehomogeneous vector spaces and their relative invariants
• A $2{\mathbf{n}}^2-{\text{log}}_2({\mathbf{n}})-1$ lower bound for the border rank of matrix multiplication
• Geometry and Complexity Theory
• Border Rank Is Not Multiplicative under the Tensor Product
• Dimension of tensor network varieties
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