Given an n-dimensional algebraA represented by a basisB and structure constants, and given a transformation matrix for a new basisC., we wish to compute the structure constants forA relative to C. There is a straightforward way to solve this problem inO(n⁵) arithmetic operations. However given an O(n_ω) matrix multiplication algorithm, we show how to solve the problem in time O(n_ω+1). Using the method of Coppersmith and Winograd, this yields an algorithm ofO(n^3.376).