On the complexity of the multiplication of matrices of small formats

Authors:
Markus Bläser
Affiliations:
Institut für Theoretische Informatik, Universität zu Lübeck, Wallstr. 40, 23560 Lübeck, Germany
Venue:
Journal of Complexity
Year:
2003

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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.