# Re: [R] Beginning Eigen System question.

Date: Wed, 23 Jun 2010 18:54:40 -0400

Eigenvectors are unique only up to a constant factor, so any scalar multiple of an eigenvector is also an eigenvector. By convention, most (all) packages normalize the eigenvectors such that their norm is 1. Therefore, eigenvectors are unique up to their sign, i.e. if (+x) is an eigenvector corresponding to an eigenvalue, then (-x) is also an eigenvector for the same eigenvalue.

Hope this helps,
Ravi.

-----Original Message-----
From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of rkevinburton_at_charter.net
Sent: Wednesday, June 23, 2010 6:32 PM
To: r-help_at_r-project.org
Subject: [R] Beginning Eigen System question.

1 3 1
1 2 2
1 1 3

//\$values
//[1] 5.000000e+00 1.000000e+00 -5.536207e-16

```//\$vectors
//           [,1]       [,2]       [,3]

//[1,] 0.5773503 -0.8451543 -0.9428090
```
//[2,] 0.5773503 -0.1690309 0.2357023
//[3,] 0.5773503 0.5070926 0.2357023

But R gives me:

```//\$vectors
//           [,1]       [,2]       [,3]

//[1,] -0.5773503 -0.8451543 -0.9428090
```
//[2,] -0.5773503 -0.1690309 0.2357023
//[3,] -0.5773503 0.5070926 0.2357023

The only difference seems to be the sign on the first eigen vector. What am I missing?

Kevin

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