julia> using AxisKeys, NamedDims, LinearAlgebra

julia> A = Symmetric(rand(2,2))
2×2 Symmetric{Float64, Matrix{Float64}}:
 0.993234  0.122844
 0.122844  0.697353

julia> K = NamedDimsArray(A, rows=[:a,:b], cols=[:c, :d])
2-dimensional NamedDimsArray(KeyedArray(...)) with keys:
↓   rows ∈ 2-element Vector{Symbol}
→   cols ∈ 2-element Vector{Symbol}
And data, 2×2 Symmetric{Float64, Matrix{Float64}}:
        (:c)       (:d)
  (:a)   0.993234   0.122844
  (:b)   0.122844   0.697353

julia> K + I
ERROR: ArgumentError: Cannot set a non-diagonal index in a symmetric matrix
Stacktrace:
 [1] setindex!
   @ /Applications/Julia-1.8.app/Contents/Resources/julia/share/julia/stdlib/v1.8/LinearAlgebra/src/symmetric.jl:227 [inlined]
 [2] setindex!
   @ ~/.julia/packages/AxisKeys/DiXQB/src/struct.jl:132 [inlined]
 [3] setindex!
   @ ~/.julia/packages/NamedDims/pu9Bn/src/wrapper_array.jl:185 [inlined]
 [4] copyto_unaliased!(deststyle::IndexCartesian, dest::NamedDimsArray{(:rows, :cols), Float64, 2, KeyedArray{Float64, 2, Symmetric{Float64, Matrix{Float64}}, Tuple{Vector{Symbol}, Vector{Symbol}}}}, srcstyle::IndexCartesian, src::NamedDimsArray{(:rows, :cols), Float64, 2, KeyedArray{Float64, 2, Symmetric{Float64, Matrix{Float64}}, Tuple{Vector{Symbol}, Vector{Symbol}}}})
   @ Base ./abstractarray.jl:1052
 [5] copyto!
   @ ./abstractarray.jl:1018 [inlined]
 [6] copy_oftype(A::NamedDimsArray{(:rows, :cols), Float64, 2, KeyedArray{Float64, 2, Symmetric{Float64, Matrix{Float64}}, Tuple{Vector{Symbol}, Vector{Symbol}}}}, #unused#::Type{Float64})
   @ LinearAlgebra /Applications/Julia-1.8.app/Contents/Resources/julia/share/julia/stdlib/v1.8/LinearAlgebra/src/LinearAlgebra.jl:377
 [7] +(A::NamedDimsArray{(:rows, :cols), Float64, 2, KeyedArray{Float64, 2, Symmetric{Float64, Matrix{Float64}}, Tuple{Vector{Symbol}, Vector{Symbol}}}}, J::UniformScaling{Bool})
   @ LinearAlgebra /Applications/Julia-1.8.app/Contents/Resources/julia/share/julia/stdlib/v1.8/LinearAlgebra/src/uniformscaling.jl:216
 [8] top-level scope
   @ REPL[8]:1

julia> function LinearAlgebra.copy_oftype(A::KeyedArray, ::Type{T}) where {T}
           return KeyedArray(LinearAlgebra.copy_oftype(A.data, T), axiskeys(A))
       end

julia> function LinearAlgebra.copy_oftype(A::NamedDimsArray, ::Type{T}) where {T}
           return NamedDimsArray(LinearAlgebra.copy_oftype(A.data, T); named_axiskeys(A)...)
       end

julia> K + I
2-dimensional NamedDimsArray(KeyedArray(...)) with keys:
↓   rows ∈ 2-element Vector{Symbol}
→   cols ∈ 2-element Vector{Symbol}
And data, 2×2 Symmetric{Float64, Matrix{Float64}}:
        (:c)       (:d)
  (:a)   1.99323    0.122844
  (:b)   0.122844   1.69735