The Geometry of Rank Decompositions of Matrix Multiplication I: 2 × 2 Matrices

DOI10.1080/10586458.2017.1403981zbMath1428.15023arXiv1610.08364OpenAlexW2963576499MaRDI QIDQ5228849

Christian Ikenmeyer, Luca Chiantini, Joseph M. Landsberg, Giorgio Ottaviani

Publication date: 13 August 2019

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.08364

zbMATH Keywords

symmetriestensor decompositiontensor rankmatrix multiplication

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Linear transformations, semilinear transformations (15A04) Multilinear algebra, tensor calculus (15A69)

Related Items (5)

Unnamed Item ⋮ Border Rank Is Not Multiplicative under the Tensor Product ⋮ The geometry of rank decompositions of matrix multiplication. II: \(3 \times 3\) matrices ⋮ Strassen's \(2 \times 2\) matrix multiplication algorithm: a conceptual perspective ⋮ On symmetries of tensor decompositions for the commutator of \(2 \times 2\) matrices

Cites Work

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• Geometric aspects of iterated matrix multiplication
• On varieties of optimal algorithms for the computation of bilinear mappings. I. The isotropy group of a bilinear mapping
• Gaussian elimination is not optimal
• Nonsplit extensions of Abelian p-groups by L 2(p n ) and general theorems on extensions of finite groups
• Linear preservers and representations with a 1-dimensional ring of invariants
• A Counterexample to Comon's Conjecture

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