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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: eigenvector
Date: Sun, 16 Jun 2013 08:38:10 +0000 (UTC)
Organization: FOGALE nanotech
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"Remus " <remusac@yahoo.com> wrote in message <kpighh$qj3$1@newscl01ah.mathworks.com>...

> 
> Hi guys,
> I'm also looking at this problem. To answer you question John, yes I know that 1p is an Eigenvector of A. Let A be a matrix which has sum of all rows = 0, then 1p (where p=dim(a)) is an eigenvector of A. 
> For Example let A = [0 0 0; -1 1 0; -1 0 1]. the comand [V,D]=eig(A) returns the following eigenvectors:
> V = [0 0 .5774; 1 0 .5774; 0 1 .5774], which is correct but as posted in the thread it is not normalized to 1.

It *is* normalized to 1

>> A = [0 0 0; -1 1 0; -1 0 1]

A =

     0     0     0
    -1     1     0
    -1     0     1

>> [V,D]=eig(A) 

V =

         0         0    0.5774
         0    1.0000    0.5774
    1.0000         0    0.5774


D =

     1     0     0
     0     1     0
     0     0     0

>>  sqrt(sum(V.^2,1)) % compute l2-norm of 3 eigen vectors 

ans =

     1     1     1

>>

% Bruno