Okay to be fair, the first post you made was not very delicately formulated also. I agree that sometimes discussions here tend towards nitpicking the way questions are formulated, but you can’t go ahead and say things like
without people getting upset.
I’m sure for the matrices you are considering there is a good algebraic reason, why trying to find the eigenvalues of smallest real part is causing issues. But I’m not qualified to judge that. KrylovKit seems to give a reason already for the Matrix in this thread here.
If you’re looking at such small matrices, you can always use the standard library package LinearAlgebra and use
julia> using LinearAlgebra
julia> sort(real(eigvals(K)))[1:4]
4-element Vector{Float64}:
-1.1102230246251565e-16
-1.1102230246251565e-16
3.9999999999999982
3.9999999999999982