Eigen not working for arbitrary precision BigFloat

[carstenbauer]

@ekiral

Would you consider it a bug of the LinearAlgebra package that I would get

julia> using LinearAlgebra
julia> matrix = [2 3; 3 0]
julia> bfmatrix = collect(BigFloat, matrix) 
julia> ishermitian(bfmatrix)
true

but I would still need to explicitly convert it to Hermitian(bfmatrix) to be able use the eigen routine?

No, that’s not a bug. ishermitian tests for hermiticity in the value not the type sense. No matter the type of a matrix, if it is hermitian ishermitian will / should return true. So, the function behaves correctly.

The fact that you need to use Hermitian(matrix) in the eigen function is because that’s a requirement from GenericLinearAlgebra. Among other things, it only adds a method eigen(A::Hermitian{<:Real}). Perhaps one could think about relaxing the function signature / dispatch constraint and, based on ishermitian / issymmetric, add a generic method that does the Hermitian(matrix) / Symmetric(matrix) type transformation automatically (i.e. for the user). Note that this is what LinearAlgebra does at some points, for example here. However, it is very natural in Julia to indiciate special properties of your matrices on the type level to dispatch to specific implementations.

In any case, not a bug.