[R] Beginning Eigen System question.

[William Revelle]

Kevin,

At 3:32 PM -0700 6/23/10, <rkevinburton at charter.net> wrote:
>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?

The sign of the eigen vectors is arbitrary.

 From ?eigen
"Recall that the eigenvectors are only defined up to a constant: even 
when the length is specified they are still only defined up to a 
scalar of modulus one (the sign for real matrices)."

Bill


>
>Kevin
>
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