Is there a reason why the following two calls to eigs order the eigenvalues
differently? The first `mat1` is numerically not symmetric but I would have
still guessed the ordering of the magnitude of the eigenvalues would be the
same as those for `mat2`?
julia> A = rand(4,4);
julia> mat1 = A.' * diagm(rand(4)) * A
4x4 Array{Float64,2}:
0.347434 0.394873 0.343693 0.214015
0.394873 0.491862 0.47723 0.383213
0.343693 0.47723 0.520122 0.513821
0.214015 0.383213 0.513821 0.665057
julia> mat2 = (mat1.' + mat1)/2;
julia> d1, = eigs(mat1, nev = 2);
julia> d2, = eigs(mat2, nev = 2);
julia> d1
2-element Array{Complex{Float64},1}:
1.70036+0.0im
0.318029+0.0im
julia> d2
2-element Array{Float64,1}:
0.318029
1.70036
