There are, but everyone uses variations of the same O(n^3) algorithm taught in college introduction to linear algebra classes because it is numerically stable and can be made extremely fast through tweaks that give spatial locality and good cache characteristics. Meanwhile the asymptomatically faster algorithms have such large constants in their big O notation that they are not worth using. FFT based matrix multiplication, which is O((n^2)log(n)), also has numerical instability on top of running slower.