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

[(Ted Harding)]

On 29-Jun-07 21:09:37, Peter Dalgaard wrote:
> Marco Visser wrote:
>> 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
>>[...]
>> 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"?

When I run it I get eigenvectors 3 and 6 both purely real.
It may be that Marco has confused this with "dominant".

Also, the eigenvalues of these two are real, and have the largest
real parts (+/- 1.3076605).

All others have complex eigenvalues, of which the real parts are
+/- 0.6538302.

It may be that Marco has been misled by this, perceiving the real
part rather than both real and complex parts, and being led to think
that the largest real part corresponds to the largest eigenvalue.

As has been clearly pointed out, this is not the way to look at it!

Ted.

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Date: 29-Jun-07                                       Time: 22:47:01
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