R help - Apr 2009 - 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.

On 4/23/2009 4:50 AM, Abelian wrote:
> 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.
It's an arbitrary choice.  See the note at the end of the Value section 
in ?eigen.

Duncan Murdoch