Re: Symbolic Calculations with Matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg74602] Re: Symbolic Calculations with Matrices*From*: dh <dh at metrohm.ch>*Date*: Wed, 28 Mar 2007 01:38:14 -0500 (EST)*References*: <euam5d$d91$1@smc.vnet.net>

Hi Sameer, your question is not very clear, but it all smells very much like discrete FFT. Therefore, I assume you want to calculate the FFT of a given finite time series f[[i]]. Well this is, besides normalization issues: Sum[f[[i]] Exp[-2 Pi I j i /n],{i,0,n-1}] This can efficiently be calculated by a dot product of f with: kernel[j_]:=Table[Exp[- 2 Pi I i j/n],{i,0,n-1}] The FFT at j can then be obtained by: kernel[j].f Or we can calculate the whole transformation matrix at once by: fftmat=Table[kernel[j],{j,0,n-1}] and obtain the fft of f by: fftmat.f Daniel sameer wrote: > Dear All, > > Greetings...I am new to Mathematica and hence my question would be > trivial to most of you. I tried to find an answer to this from the > previuos posts but unfortunately I could n't locate any answer. > > I have to do various matrix operation like derivatives, inverse etc, > where each element of the matrix is a matrix/vector. {eg. 1, > exp(j2*pi*/N), exp(j3*pi*/N)...., exp(j((N-1)*pi*/N} or it could be an > FFT matrix. > > My question is how can I specify such vectors or matrices with the > range of values as symbolic expressions in the range, 0 to N-1. > > Any help is greatly appreciated.. > > With Thanks and Best Regards > > Sameer > >