Eigenvectors differ between julia and Wolfram/Delphi

Specific Domains Numerics
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1

I am trying to find the eigenvectors of a matrix:

t = [124.70244538509718 -120.72494594206698; -120.72494594206698 122.53090477427045]

Using eigvecs from linear algebra, I get

 eigvecs(t)
2×2 Matrix{Float64}:
 -0.70392   -0.710279
 -0.710279   0.70392

This disagrees with the value a colleague gets in Delphi, as well as with Mathematics/WolframAlpha computes:

normalize(eigenvectors {{124.70244538509718,-120.72494594206698},{-120.72494594206698,122.53090477427045}})

returns Wolfram

I am not super clear why this is happening. Any advice?

2

Can you be more specific about what’s wrong? Note that generally eigenvectors have somewhat arbitrary sign and order. If you multiply an eigenvector by -1 (or any scalar really), it’s still an eigenvector. The order is usually determined by and agrees with how the eigenvalues are sorted, e.g. by magnitude or real part. Some applications/packages sort eigenvalues, but you have to look at the documentation to find out whether and how.

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3

WolframAlpha is returning equivalent eigenvectors to Julia’s, just in the opposite order and with the opposite signs. As @apo383 noted, they are both valid answers — there is no universal convention for the ordering and the overall scaling of eigenvectors.

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