Message-ID: <49F058AB.2080402@stats.uwo.ca>
Date: 2009-04-23T12:01:47Z
From: Duncan Murdoch
Subject: the definition of eigenvector in R
In-Reply-To: <7f6157e8-7c3b-43d6-82ab-4271cb28faa4@x31g2000prc.googlegroups.com>
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