Dear Erich,
As I am sure you are aware, if x is an eigenvector corresponding to an
eigenvalue lambda, then alpha*x, where alpha is a nonzero scalar, is
also an eigenvector corresponding to lambda. So, in particular we can
choose alpha = +1 or 1. The LAPACK symmetric eigenvalue routines
return orthonormal eigenvectors, so that in particular norm(x) = 1,
where norm is the 2norm (Euclidean length), but do not choose any other
scaling to further particularise x.
Best wishes,
Sven Hammarling.
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