[R] eigenvalues of a circulant matrix
Globe Trotter
itsme_410 at yahoo.com
Mon May 2 05:10:55 CEST 2005
Hi,
It is my understanding that the eigenvectors of a circulant matrix are given as
follows:
1,omega,omega^2,....,omega^{p-1}
where the matrix has dimension given by p x p and omega is one of p complex
roots of unity. (See Bellman for an excellent discussion on this).
The matrix created by the attached row and obtained using the following
commands
indicates no imaginary parts for the eigenvectors. It appears that the real
values are close, but not exactly so, and there is no imaginary part
whatsoever.
x<-scan("kinv.dat") #length(x) = 216
y<-x[c(109:216,1:108)]
X<-toeplitz(y)
eigen(X)$vectors
Note that the eigenvectors are correct, and they are indeed real, because X is
symmetric.
Is this a bug in R? Any insight if not, please!
Many thanks and best wishes!
This is unrelated, but can the R-help archive maintainers please not put e-mail
addresses in the archive? This would really help people like me who would like
to post using their professional e-mail addresses. Just stripping the e-mail
address from everything else would be great, or make it non-spammable by adding
some random number or something which would be obvious to anyone reading it
without the help of a machine. After all, why give spider programs more fodder?
Best wishes!
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