This is a theoretical result - for now at least. Theoretically the fastest linear solvers run in time n^w where w ~ 2.3 is the matrix multiplication constant. I

This is a theoretical result - for now at least. Theoretically the fastest linear solvers run in time n^w where w ~ 2.3 is the matrix multiplication constant. In practice the fast matrix multiplication algorithms are not that fast, so they aren't used for linear solvers.