R and Mathematica software differ when computing fft(c(1,1))
and Fourier[{1,1}]
,
2+0i 0+0i
and
{1.41421+ 0i, 0} respectively. How can this be????
R and Mathematica software differ when computing 2+0i 0+0i and {1.41421+ 0i, 0} respectively. How can this be???? 

closed as off topic by Gerald Edgar, Yemon Choi, Torsten Ekedahl, Felipe Voloch, Andres Caicedo Jul 30 '11 at 22:21Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question. 


Normalizing factor. It looks like R defines the Discrete Fourier Transform matrix as $F = [1$ $1; 1$ $1]$ while Mathematica defines it as $F = \frac{1}{\sqrt{2}}[1$ $1; 1$ $1]$. If you do inverse fft  R would define it to be $F^{1} = \frac{1}{2}[1$ $1; 1$ $1]$ while Mathematica would define it as $F^{1} = F^{H} = \frac{1}{\sqrt{2}}[1$ $1; 1$ $1]$ where $H$ is Hermitian transpose. 

