International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. B, ch. 1.3, p. 55

The DFT was defined in Section 1.3.2.7.4 in an ndimensional setting and it was shown that when the decimation matrix N is diagonal, say , then has a tensor product structure: This may be rewritten as follows: where the I's are identity matrices and × denotes ordinary matrix multiplication. The matrix within each bracket represents a onedimensional DFT along one of the n dimensions, the other dimensions being left untransformed. As these matrices commute, the order in which the successive 1D DFTs are performed is immaterial.
This is the most straightforward method for building an ndimensional algorithm from existing 1D algorithms. It is known in crystallography under the name of `Beevers–Lipson factorization' (Section 1.3.4.3.1), and in signal processing as the `row–column method'.