[R] Beginning Eigen System question.

[Ravi Varadhan]

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.

Forgive me if I missunderstand a basic Eigensystem but when I present the
following matrix to most any other LinearAlgebra system:

 1  3  1
 1  2  2
 1  1  3

I get an answer like:

//$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:

//$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

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

Kevin

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