From: Globe Trotter <itsme_410_at_yahoo.com>

Date: Mon 02 May 2005 - 23:35:55 EST

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 23:45:35 2005

Date: Mon 02 May 2005 - 23:35:55 EST

x<-scan("kinv")

y<-x[c(109:1,2:108)]

X=toeplitz(y)

Z=y

for (i in 2:216) Z=rbind(Z,y[c((216-i+2):216,1:(216-i+1))])

- Prof Brian Ripley <ripley@stats.ox.ac.uk> wrote:

> On Sun, 1 May 2005, someone who didn't give his name wrote:

*>**> > 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).**>**> What is the relevance of this? Also, your reference is useless to us,**> which is important as this all hinges on your definitions.**>**> > 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**>**> We don't have "kinv.dat", but X is not circulant as usually defined.**>**> > 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!**>**> Well, first R calls LAPACK or EISPACK, so it would be a bug in one of**> those. But in so far as I understand you, X is a real symmetric matrix,**> and those have real eigenvalues and eigenvectors.**>**> I think you are confused about the meaning of Toeplitz and circulant.**> Compare**>**> http://mathworld.wolfram.com/CirculantMatrix.html**> http://mathworld.wolfram.com/ToeplitzMatrix.html**>**> and note that ?toeplitz says it computes the *symmetric* Toeplitz matrix.**>**> There is a very regretable tendency here for people to assume their**> lack of understanding is `a bug in R'.**>**> --**> Brian D. Ripley, ripley@stats.ox.ac.uk**> Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/**> University of Oxford, Tel: +44 1865 272861 (self)**> 1 South Parks Road, +44 1865 272866 (PA)**> Oxford OX1 3TG, UK Fax: +44 1865 272595**>*

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 23:45:35 2005

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