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???? 


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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. 

