Dear All,
I am working on Fourier transforms, and
therefore I want to evaluate the exponential of a matrix, say
E=exp(A+iB). The matrices A and B do not
commute, hence (I guess!) the exponential cannot be split into real and
imaginary parts explicitly.
Equivalently, I could be looking for the
eigenvalues and eigenvectors of the matrix A+iB; the exponential is then
calculated trivially.
I have tried the Taylor expansion
exp(A+iB)=sum([A+iB]^n/n!,n=0..Inf), but the numerical errors become explosive
very quickly.
Ox does not seem to accept a complex matrix as
an input, in the eigen() function (It has to be mXm not 2mXm). Does anyone
know any trick for solving this kind of eigenproblems? For instance, any
relations between the eigenvalues and -vectors of the matrix A+iB with the
eigenvalues and -vectors of its components A and B would be very helpful. Can
this complex eigenproblem be represented into an eigenproblem where the
matrices are real valued?
Thanks in advance,
Kyriakos
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Kyriakos M. Chourdakis
Dept. of Economics,
QMW College,
London
