Matrix Multiplication, Approximately.

We provide a brief overview of the history of matrix multiplication algorithms to make the field more accessible at the undergraduate level, as well as for researchers who do not have a lot of background knowledge in the area. We explore algorithms for matrix multiplication, discuss concepts and questions central to the field, and consider the unifying design strategy behind modern fast matrix multiplication algorithms. Furthermore, we examine the critical flaw of most modern matrix multiplication algorithms regarding practical implementation. Then, in the interest of discussing practical fast matrix multiplication algorithms, we briefly investigate the subfield of approximate matrix multiplication algorithms. That is, the field of matrix multiplication where, instead of computing the exact product of two matrices, an approximate product is calculated. Moreover, we delve into the technical details of the Drineas-Kannan fast Monte Carlo approximate matrix multiplication algorithm, as well as discuss its practical applications to large sets of data.