[R] Dominant eigenvector displayed as third (Marco Visser)

[Peter Dalgaard]

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.
>   
????

I get

 > eigen(mat)$values
[1] -0.65383+1.132467i -0.65383-1.132467i  0.65383+1.132467i  
0.65383-1.132467i
[5] -1.30766+0.000000i  1.30766+0.000000i
 > Mod(eigen(mat)$values)
[1] 1.307660 1.307660 1.307660 1.307660 1.307660 1.307660

So all the eigenvalues are equal in modulus. What makes you think one of 
them is "dominant"?