It's straightforward to show that exp(d/dz)f(z) = f(z+1). If we think of a D-dimensional column vector as a function from the set {0, 1, ..., D-1} to the complex numbers, then the circulant matrix |0 1 0 ... 0 0| |0 0 1 ... 0 0| |. . . . . .| |. . . . . .| |. . . . . .| |0 0 0 ... 1 0| |0 0 0 ... 0 1| |1 0 0 ... 0 0| applied to the column vector f computes f((z+1) mod D), where 0 <= z < D. The eigenvectors of this matrix are "plane waves" and form the columns of the discrete fourier transform in D dimensions. I'm interested in finding a DxD matrix "d/dz" such that exp("d/dz") is the matrix above; it'll have {0, 1, ..., D-1} as eigenvalues (or perhaps {-(D-1)/2, ..., 0, ..., (D-1)/2}). I can solve for "d/dz" numerically, but I've been bitten before by the branch cut when taking matrix logs and looking for patterns. Is there a general formula for "d/dz" in dimension D? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com