International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 51

By virtue of definitions (i) and (ii),so that and may be represented, in the canonical bases of and , by the following matrices:
When N is symmetric, and may be identified in a natural manner, and the above matrices are symmetric.
When N is diagonal, say , then the tensor product structure of the full multidimensional Fourier transform (Section 1.3.2.4.2.4)gives rise to a tensor product structure for the DFT matrices. The tensor product of matrices is defined as follows:Let the index vectors and be ordered in the same way as the elements in a Fortran array, e.g. for with increasing fastest, next fastest, slowest; thenwhereandwhere