Lectures 1 and 2 Matrix Multiplication and Matrix Inversion 1 Prior Work on Matrix Multiplication

There has been much effort to improve the runtime of matrix multiplication. The trivial algorithm multiplies n×n matrices in O(n) time. Strassen (’69) surprised everyone by giving an O(n) time algorithm. This began a long line of improvements until in 1986, Coppersmith and Winograd achieved O(n). After 24 years of no progress, in 2010 Andrew Stothers, a graduate student in Edinburgh, improved the running time to O(n). In 2011, Virginia Williams got O(n), which was the best bound until Le Gall got O(n) in 2014. Many believe that the ultimate bound will be n, but this has yet to be proven.