A New Algorithm for Inner Product

Abstract—In this note we describe a new way of computing the inner product of two vectors. This method cuts down the number of multiplications required when we want to perform a large number of inner products on a smaller set of vectors. In particular, we obtain that the product of two n×n matrices can be performed using roughly n 3 /2 multiplications instead of the n 3 multiplications which the regular method necessitates.