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

[Spencer Graves]

      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.  
>
>
>
>
>        
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