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We show that the border support rank of the tensor corresponding to two-by-two matrix multiplication is seven over the complex numbers.
Gaussian elimination is not optimal
Volker Strassen · 1969
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On minimizing the number of multiplications necessary for matrix multiplication
John E. Hopcroft and Leslie R. Kerr · 1971
Earlier work this paper cites.
On multiplication of 2 × 2 2\times 2 matrices
Shmuel Winograd · 1971
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On varieties of optimal algorithms for the computation of bilinear mappings II. optimal algorithms for 2 × 2 2\times 2 -matrix multiplication
Hans F. de Groote · 1978
Earlier work this paper cites.
Geometrische Methoden in der Invariantentheorie
Hanspeter Kraft · 1984
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Tensor rank is NP-complete
Johan Håstad · 1990
Earlier work this paper cites.
Algebraic complexity theory, volume 315 of Grundlehren der Mathematischen Wissenschaften, 1997
Peter Bürgisser, Michael Clausen, and M. Amin Shokrollahi · 1997
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Nondeterministic quantum query and communication complexities
Ronald de Wolf · 2003
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On the Ideals of Secant Varieties of Segre Varieties
Joseph M. Landsberg and Laurent Manivel · 2004
Cited alongside, same era.
The border rank of the multiplication of 2 × 2 2\times 2 matrices is seven
J. M. Landsberg · 2006
Cited alongside, same era.
Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers
Avi Berman, Shmuel Friedland, Leslie Hogben, Uriel G. Rothblum, and Bryan Shader · 2008
Cited alongside, same era.
Computing Multiplicities of Lie Group Representations
Matthias Christandl, Brent Doran, and Michael Walter · 2012
Cited alongside, same era.
Secant varieties of Segre–Veronese varieties
Claudiu Raicu · 2012
Cited alongside, same era.
Powers of Tensors and Fast Matrix Multiplication
François Le Gall · 2014
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Algorithms and Complexity in Algebraic Geometry, Fall 2014: Computational open questions
2014
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Schur Group Theory Software (Version 6.02) , 2014
Brian G. Wybourne, Franck Butelle, Ronald King, and Frédéric Toumazet · 2014
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Talk: Matrix Rank – Extensions, Applications and Open Problems , 2014
Avi Wigderson · 2014
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The complexity of computing the minimum rank of a sign pattern matrix
Amey Bhangale and Swastik Kopparty · 2015
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Henry Cohn and Christopher Umans · 2013
Cited alongside, same era.
Equations for lower bounds on border rank
Jonathan D. Hauenstein, Christian Ikenmeyer, and Joseph M. Landsberg · 2013
Cited alongside, same era.
Geometric complexity theory, tensor rank, and Littlewood-Richardson coefficients
Christian Ikenmeyer · 2013
Cited alongside, same era.
Software
SageMath, the Sage Mathematics Software System (Version 7.2)
Cited in the paper.
Macaulay2 package
SchurFunctors – for computing Schur functors
Cited in the paper.
Brian Hall · 2015
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Yaroslav Shitov · 2016
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Harry Buhrman, Matthias Christandl, and Jeroen Zuiddam · 2017
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