There is no dominant eigenvalue: The eigenvalues of that matrix are the 6 different roots of 5. All have modulus (or absolute value) = 1.307660. When I raised them all to the 6th power, all 6 were 5+0i.
Someone else can tell us why this is, but this should suffice as an initial answer to your question. Hope this helps. Spencer Graves Marco Visser wrote: > Dear R users & Experts, > > This is just a curiousity, I was wondering why the dominant eigenvetor and > eigenvalue > of the following matrix is given as the third. I guess this could complicate > automatic selection > procedures. > > 0 0 0 0 0 5 > 1 0 0 0 0 0 > 0 1 0 0 0 0 > 0 0 1 0 0 0 > 0 0 0 1 0 0 > 0 0 0 0 1 0 > > Please copy & paste the following into R; > > a=c(0,0,0,0,0,5,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0) > mat=matrix(a, ncol=6,byrow=T) > eigen(mat) > > The matrix is a population matrix for a plant pathogen (Powell et al 2005). > > Basically I would really like to know why this happens so I will know if it > can occur > again. > > Thanks for any comments, > > Marco Visser > > > Comment: In Matlab the the dominant eigenvetor and eigenvalue > of the described matrix are given as the sixth. Again no idea why. > > reference > > J. A. Powell, I. Slapnicar and W. van der Werf. Epidemic spread of a > lesion-forming > plant pathogen - analysis of a mechanistic model with infinite age structure. > (2005) > Linear Algebra and its Applications 298. p 117-140. > > > > > > ____________________________________________________________________________________Ready > for the edge of your seat? > Check out tonight's top picks on Yahoo! TV. > > [[alternative HTML version deleted]] > > ______________________________________________ > 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 > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ 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 and provide commented, minimal, self-contained, reproducible code.