eigen(nda) eigvals(nda), and Xdet(nda) are broken

[mzgubic]

julia> A = rand(4, 4);

julia> corr = A * A';

julia> nda = NamedDimsArray{(:a, :a)}(corr);

julia> eigen(nda)
ERROR: MethodError: no method matching eigen!(::NamedDimsArray{(:a, :a), Float64, 2, Matrix{Float64}}; permute=true, scale=true, sortby=LinearAlgebra.eigsortby)
Closest candidates are:
  eigen!(::SymTridiagonal{var"#s859", V} where {var"#s859"<:Union{Float32, Float64}, V<:AbstractVector{var"#s859"}}) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/tridiag.jl:284 got unsupported keyword arguments "permute", "scale", "sortby"
  eigen!(::SymTridiagonal{var"#s859", V} where {var"#s859"<:Union{Float32, Float64}, V<:AbstractVector{var"#s859"}}, ::UnitRange) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/tridiag.jl:287 got unsupported keyword arguments "permute", "scale", "sortby"
  eigen!(::SymTridiagonal{var"#s859", V} where {var"#s859"<:Union{Float32, Float64}, V<:AbstractVector{var"#s859"}}, ::Real, ::Real) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/tridiag.jl:292 got unsupported keyword arguments "permute", "scale", "sortby"
  ...
Stacktrace:
 [1] eigen(A::NamedDimsArray{(:a, :a), Float64, 2, Matrix{Float64}}; permute::Bool, scale::Bool, sortby::typeof(LinearAlgebra.eigsortby))
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/eigen.jl:237
 [2] eigen(A::NamedDimsArray{(:a, :a), Float64, 2, Matrix{Float64}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/eigen.jl:235
 [3] top-level scope
   @ REPL[35]:1

julia> det(nda)
ERROR: MethodError: no method matching logabsdet(::NamedDims.NamedFactorization{(:a, :a), Float64, LU{Float64, Matrix{Float64}}})
Closest candidates are:
  logabsdet(::SymTridiagonal; shift) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/tridiag.jl:446
  logabsdet(::UnitUpperTriangular{T, S} where S<:AbstractMatrix{T}) where T at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/triangular.jl:2545
  logabsdet(::UnitLowerTriangular{T, S} where S<:AbstractMatrix{T}) where T at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/triangular.jl:2546
  ...
Stacktrace:
 [1] det(F::NamedDims.NamedFactorization{(:a, :a), Float64, LU{Float64, Matrix{Float64}}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/factorization.jl:51
 [2] det(A::NamedDimsArray{(:a, :a), Float64, 2, Matrix{Float64}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/generic.jl:1557
 [3] top-level scope
   @ REPL[36]:1

julia> logdet(nda)
ERROR: MethodError: no method matching logabsdet(::NamedDims.NamedFactorization{(:a, :a), Float64, LU{Float64, Matrix{Float64}}})
Closest candidates are:
  logabsdet(::SymTridiagonal; shift) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/tridiag.jl:446
  logabsdet(::UnitUpperTriangular{T, S} where S<:AbstractMatrix{T}) where T at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/triangular.jl:2545
  logabsdet(::UnitLowerTriangular{T, S} where S<:AbstractMatrix{T}) where T at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/triangular.jl:2546
  ...
Stacktrace:
 [1] logabsdet(A::NamedDimsArray{(:a, :a), Float64, 2, Matrix{Float64}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/generic.jl:1595
 [2] logdet(A::NamedDimsArray{(:a, :a), Float64, 2, Matrix{Float64}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/generic.jl:1618
 [3] top-level scope
   @ REPL[39]:1

julia> logabsdet(nda)
ERROR: MethodError: no method matching logabsdet(::NamedDims.NamedFactorization{(:a, :a), Float64, LU{Float64, Matrix{Float64}}})
Closest candidates are:
  logabsdet(::SymTridiagonal; shift) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/tridiag.jl:446
  logabsdet(::UnitUpperTriangular{T, S} where S<:AbstractMatrix{T}) where T at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/triangular.jl:2545
  logabsdet(::UnitLowerTriangular{T, S} where S<:AbstractMatrix{T}) where T at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/triangular.jl:2546
  ...
Stacktrace:
 [1] logabsdet(A::NamedDimsArray{(:a, :a), Float64, 2, Matrix{Float64}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/generic.jl:1595
 [2] top-level scope
   @ REPL[40]:1

I think we can just defer to parent, rather than use NamedFactorization, because the eigenvectors and eigenvalues will not have a dimension name of the original matrix.