[R] eigenvalues of a circulant matrix

From: Globe Trotter <itsme_410_at_yahoo.com>
Date: Mon 02 May 2005 - 13:10:55 EST


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!






R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Mon May 02 13:19:26 2005

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