Order of eigenvectors of (symmetric) 2x2 matrices

[dkarrasch]

I guess the following is a (quite scary) bug:

using LinearAlgebra, StaticArrays, Test
S = SMatrix{2,2}((70., 0., 0., 1/70))
E = eigen(S)
Λs = eigvals(E)
V = eigvecs(E)
@test S * V  ≈ V * Diagonal(eigvals(E))
M = Matrix(S)
F = eigen(M)
Λm = eigvals(F)
@test Λs ≈ Λm
U = eigvecs(F)
@test M * U ≈ U * Diagonal(eigvals(F))

I thought one should be able to rely on that eigvecs(E)[:,1] is the eigenvector corresponding to eigvals(E)[1], like in the normal matrix case? Or how would one do that otherwise?

[dkarrasch]

This turns out to be specific for the case when the off-diagonal terms are zero, so not that scary after all. In that case, one may simply reorder the identity tensor according to the order of the diagonal entries, as suggested by @fredrikekre in the corresponding Tensors.jl issue. I can translate his PR here once that is reviewed and verified.