On the complexity of the multiplication of matrices of small formats

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Markus Bläser

Published: 2003, Last Modified: 10 May 2024J. Complex. 2003EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We prove a lower bound of 2mn+2n−m−2 for the bilinear complexity of the multiplication of n×m-matrices with m×n-matrices using the substitution method (m⩾n⩾3). In particular, we obtain the improved lower bound of 19 for the bilinear complexity of 3×3-matrix multiplication.