Designing Strassen's algorithm [article]

Joshua A. Grochow, Cristopher Moore
2017 arXiv   pre-print
In 1969, Strassen shocked the world by showing that two n x n matrices could be multiplied in time asymptotically less than O(n^3). While the recursive construction in his algorithm is very clear, the key gain was made by showing that 2 x 2 matrix multiplication could be performed with only 7 multiplications instead of 8. The latter construction was arrived at by a process of elimination and appears to come out of thin air. Here, we give the simplest and most transparent proof of Strassen's
more » ... rithm that we are aware of, using only a simple unitary 2-design and a few easy lines of calculation. Moreover, using basic facts from the representation theory of finite groups, we use 2-designs coming from group orbits to generalize our construction to all n (although the resulting algorithms aren't optimal for n at least 3).
arXiv:1708.09398v1 fatcat:i7txv335gnbexjakfc7dl2euoa