Journal of the Operations Research Society of China ›› 2020, Vol. 8 ›› Issue (1): 29-43.doi: 10.1007/s40305-019-00280-x

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An Introduction to the Computational Complexity of Matrix Multiplication

Yan Li1, Sheng-Long Hu2, Jie Wang3, Zheng-Hai Huang1   

  1. 1 School of Mathematics, Tianjin University, Tianjin 300350, China;
    2 Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China;
    3 College of Science, China Jiliang University, Hangzhou 310018, China
  • Received:2018-10-09 Revised:2019-02-26 Online:2020-03-30 Published:2020-02-18
  • Contact: Sheng-Long Hu, Yan Li, Jie Wang, Zheng-Hai Huang E-mail:shenglonghu@hdu.edu.cn;yanlee@tju.edu.cn;jiewang@cjlu.edu.cn;huangzhenghai@tju.edu.cn

Abstract: This article introduces the approach on studying the computational complexity of matrix multiplication by ranks of the matrix multiplication tensors. Basic results and recent developments in this area are reviewed.

Key words: Matrix multiplication, Computational complexity, Tensor rank, Bilinear mapping, Border rank

CLC Number: