Journal or Book Title
Applicable Algebra in Engineering, Communication and Computing
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(nω) matrix multiplication algorithm, we show how to solve the problem in time O(nω+1). Using the method of Coppersmith and Winograd, this yields an algorithm ofO(n3.376).
Hentzel, Irvin R. and Jacobs, David Pokrass, "Fast change of basis in algebras" (1992). Mathematics Publications. 139.