Kevin,
At 3:32 PM -0700 6/23/10, <rkevinbur...@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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