论文信息 - The Rank of $n\times n$ Matrix Multiplication is at least 3n^2-2\sqrt{2}n^3/2-3n

The Rank of $n\times n$ Matrix Multiplication is at least 3n^2-2\sqrt{2}n^3/2-3n

Abstract We prove that the rank of the n × n matrix multiplication is at least 3 n 2 - 2 2 n 3 2 - 3 n . The previous bounds were 3 n 2 - 4 n 3 2 - n due to Landsberg [2] and 5 2 n 2 - 3 n due to Blaser [1] . Our bound improves the previous bounds for any n ⩾ 24 .

Emanuele Raviolo | Alex Massarenti

[1] V. Strassen. Gaussian elimination is not optimal , 1969 .

[2] J. Landsberg. Tensors: Geometry and Applications , 2011 .

[3] J. M. Landsberg,et al. New Lower Bounds for the Rank of Matrix Multiplication , 2012, SIAM J. Comput..

[4] V. Strassen. Rank and optimal computation of generic tensors , 1983 .

[5] Markus Bläser. A 5/2 n2-Lower Bound for the Rank of n×n Matrix Multiplication over Arbitrary Fields , 1999, FOCS.