cholesky of a Symmetric KeyedArray strips out the Symmetric

[sdl1]

Hello, I got tripped up by this:

julia> X = Symmetric(KeyedArray([1.0 0.1; 0.2 1.0], ([:a, :b], [:a, :b])))
2×2 Symmetric{Float64, KeyedArray{Float64, 2, Matrix{Float64}, Tuple{Vector{Symbol}, Vector{Symbol}}}}:
 1.0  0.1
 0.1  1.0

julia> isposdef(X) # Doesn't give expected answer
false

julia> isposdef(collect(X)) # Gives expected answer
true

Note that

julia> X = Symmetric([1.0 0.1; 0.2 1.0])
2×2 Symmetric{Float64, Matrix{Float64}}:
 1.0  0.1
 0.1  1.0

julia> isposdef(X) # Gives expected answer
true

As far as I can tell, this is because we reach this method in this package:

LinearAlgebra.cholesky(A::Hermitian{T, <:KeyedArray{T}}; kwargs...) where {T} =
    cholesky(parent(A); kwargs...)

And

julia> parent(Hermitian(X))
2-dimensional KeyedArray(...) with keys:
↓   2-element Vector{Symbol}
→   2-element Vector{Symbol}
And data, 2×2 Matrix{Float64}:
        (:a)  (:b)
  (:a)   1.0   0.1
  (:b)   0.2   1.0

which does not satisfy isposdef since it's not Hermitian.

This is with AxisKeys v0.1.22 and julia v1.6.0