New lower bounds for the rank of matrix multiplication

V. Strassen, Rank and optimal computation of generic tensors , Linear Algebra Appl. 52/53

1983

Earlier work this paper cites.

Thomas Lehmkuhl and Thomas Lickteig, On the order of approximation in approximative triadic decompositions of tensors , Theoret. Comput. Sci. 66

1989

Earlier work this paper cites.

Peter Bürgisser, Michael Clausen, and M. Amin Shokrollahi, Algebraic complexity theory , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 315, Springer-Verlag, Berlin, 1997, With the collaboration of Thomas Lickteig. MR 99c:68002

1997

Earlier work this paper cites.

Markus Bläser, A 5 2 ​ n 2 \frac{5}{2}n^{2} -lower bound for the rank of n × n n\times n -matrix multiplication over arbitrary fields , 40th Annual Symposium on Foundations of Computer Science (New York, 1999), IEEE Computer Soc., Los Alamitos, CA, 1999, pp. 45–50. MR MR1916183

1999

Cited alongside, same era.

by same author, On the complexity of the multiplication of matrices of small formats , J. Complexity 19

2003

Cited alongside, same era.

J.M. Landsberg and Giorgio Ottaviani, New lower bounds for the border rank of matrix multiplication , preprint, arXiv:1112.6007

Original

Cited in the paper.

Alex Massarenti and Emanuele Raviolo, Erratum to: The rank of n × n n\times n matrix multiplication is at least 3 ​ n 2 − 2 ​ 2 ​ n 3 / 2 − 3 ​ n 3n^{2}-2\sqrt{2}n^{3}/2-3n , to appear

Cited in the paper.

J. M. Landsberg, Tensors: geometry and applications , Graduate Studies in Mathematics, vol. 128, American Mathematical Society, Providence, RI, 2012. MR 2865915

2012

Closest in time.

by same author, The rank of n × n n\times n matrix multiplication is at least 3 ​ n 2 − 2 ​ 2 ​ n 3 2 − 3 ​ n 3n^{2}-2\sqrt{2}n^{\frac{3}{2}}-3n , Linear Algebra Appl. 438

2013

Closest in time.