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Message-ID: <7f6157e8-7c3b-43d6-82ab-4271cb28faa4@x31g2000prc.googlegroups.com>
Date: 2009-04-23T08:50:07Z
From: Abelian
Subject: the definition of eigenvector in R

Dear All
i have a little puzzle about eigenvector in the R.
As we know that the eigenvector can be displayed on several form.
For example

A=matrix(c(1,2,4,3),2,2)
if we want to get the eigenvalue and eigenvector, the code followed
eigen(A)

$values
[1]  5 -1

$vectors
           [,1]       [,2]
[1,] -0.7071068 -0.8944272
[2,] -0.7071068  0.4472136

however, we also can calculate the vector matrix such that
$vectors
           [,1]       [,2]
[1,] 0.7071068 -0.8944272
[2,] 0.7071068  0.4472136

or

$vectors
           [,1]       [,2]
[1,] -0.7071068  0.8944272
[2,] -0.7071068 -0.4472136

or

$vectors
           [,1]       [,2]
[1,] 0.7071068   0.8944272
[2,] 0.7071068  -0.4472136

my puzzle is that what does the rule be followed in R?
On the other word, what does it make the R to display the first form?
thanks a lot.