diff --git a/src/wrappers.jl b/src/wrappers.jl
index 7145ff9..7bb0e89 100644
--- a/src/wrappers.jl
+++ b/src/wrappers.jl
@@ -32,19 +32,24 @@ end
       $(Expr(:new, :(Base.LogicalIndex{T, typeof(mask)}), :mask, :(A.sum)))
 end
 
-adapt_structure(to, A::Adjoint) = adjoint(adapt(to, Base.parent(A)))
-adapt_structure(to, A::Transpose) = transpose(adapt(to, Base.parent(A)))
-adapt_structure(to, A::LowerTriangular) = LowerTriangular(adapt(to, Base.parent(A)))
-adapt_structure(to, A::UnitLowerTriangular) = UnitLowerTriangular(adapt(to, Base.parent(A)))
-adapt_structure(to, A::UpperTriangular) = UpperTriangular(adapt(to, Base.parent(A)))
-adapt_structure(to, A::UnitUpperTriangular) = UnitUpperTriangular(adapt(to, Base.parent(A)))
-adapt_structure(to, A::Diagonal) = Diagonal(adapt(to, Base.parent(A)))
-adapt_structure(to, A::Bidiagonal) = Bidiagonal(adapt(to, A.dv), adapt(to, A.ev), Symbol(A.uplo))
-adapt_structure(to, A::Tridiagonal) = Tridiagonal(adapt(to, A.dl), adapt(to, A.d), adapt(to, A.du))
-adapt_structure(to, A::SymTridiagonal) = SymTridiagonal(adapt(to, A.dv), adapt(to, A.ev))
-adapt_structure(to, A::Symmetric) = Symmetric(adapt(to, Base.parent(A)), Symbol(A.uplo))
-adapt_structure(to, A::Hermitian) = Hermitian(adapt(to, Base.parent(A)), Symbol(A.uplo))
-adapt_structure(to, A::UpperHessenberg) = UpperHessenberg(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.Adjoint) =
+      LinearAlgebra.adjoint(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.Transpose) =
+      LinearAlgebra.transpose(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.LowerTriangular) =
+      LinearAlgebra.LowerTriangular(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.UnitLowerTriangular) =
+      LinearAlgebra.UnitLowerTriangular(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.UpperTriangular) =
+      LinearAlgebra.UpperTriangular(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.UnitUpperTriangular) =
+      LinearAlgebra.UnitUpperTriangular(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.Diagonal) =
+      LinearAlgebra.Diagonal(adapt(to, Base.parent(A)))
+adapt_structure(to, A::LinearAlgebra.Tridiagonal) =
+      LinearAlgebra.Tridiagonal(adapt(to, A.dl), adapt(to, A.d), adapt(to, A.du))
+adapt_structure(to, A::LinearAlgebra.Symmetric) =
+      LinearAlgebra.Symmetric(adapt(to, Base.parent(A)))
 
 
 # we generally don't support multiple layers of wrappers, but some occur often
@@ -88,19 +93,15 @@ const WrappedArray{T,N,Src,Dst} = Union{
       #Base.ReshapedArray{T,N,<:Src},
       #Base.ReinterpretArray{T,N,<:Any,<:Src},
 
-      Adjoint{T,<:Src},    # The adjoint/transpose of a Vector has shape 1xN, so is a 2d
-      Transpose{T,<:Src},  # wrapper around a 1d array, hence use Src not Dst
-      LowerTriangular{T,<:Dst},
-      UnitLowerTriangular{T,<:Dst},
-      UpperTriangular{T,<:Dst},
-      UnitUpperTriangular{T,<:Dst},
-      Diagonal{T,<:Src},
-      Bidiagonal{T,<:Src},
-      Tridiagonal{T,<:Src},
-      SymTridiagonal{T,<:Src},
-      Symmetric{T,<:Dst},
-      Hermitian{T,<:Dst},
-      UpperHessenberg{T,<:Dst},
+      LinearAlgebra.Adjoint{T,<:Dst},
+      LinearAlgebra.Transpose{T,<:Dst},
+      LinearAlgebra.LowerTriangular{T,<:Dst},
+      LinearAlgebra.UnitLowerTriangular{T,<:Dst},
+      LinearAlgebra.UpperTriangular{T,<:Dst},
+      LinearAlgebra.UnitUpperTriangular{T,<:Dst},
+      LinearAlgebra.Diagonal{T,<:Dst},
+      LinearAlgebra.Tridiagonal{T,<:Dst},
+      LinearAlgebra.Symmetric{T,<:Dst},
 
       WrappedReinterpretArray{T,N,<:Src},
       WrappedReshapedArray{T,N,<:Src},
@@ -120,31 +121,20 @@ const WrappedArray{T,N,Src,Dst} = Union{
 
 # accessors for extracting information about the wrapper type
 ndims(::Type{<:Base.LogicalIndex}) = 1
-ndims(::Type{<:Adjoint}) = 2
-ndims(::Type{<:Transpose}) = 2
-ndims(::Type{<:LowerTriangular}) = 2
-ndims(::Type{<:UnitLowerTriangular}) = 2
-ndims(::Type{<:UpperTriangular}) = 2
-ndims(::Type{<:UnitUpperTriangular}) = 2
-ndims(::Type{<:Diagonal}) = 2
-ndims(::Type{<:Bidiagonal}) = 2
-ndims(::Type{<:Tridiagonal}) = 2
-ndims(::Type{<:SymTridiagonal}) = 2
-ndims(::Type{<:Symmetric}) = 2
-ndims(::Type{<:Hermitian}) = 2
-ndims(::Type{<:UpperHessenberg}) = 2
+ndims(::Type{<:LinearAlgebra.Adjoint}) = 2
+ndims(::Type{<:LinearAlgebra.Transpose}) = 2
+ndims(::Type{<:LinearAlgebra.LowerTriangular}) = 2
+ndims(::Type{<:LinearAlgebra.UnitLowerTriangular}) = 2
+ndims(::Type{<:LinearAlgebra.UpperTriangular}) = 2
+ndims(::Type{<:LinearAlgebra.UnitUpperTriangular}) = 2
+ndims(::Type{<:LinearAlgebra.Diagonal}) = 2
+ndims(::Type{<:LinearAlgebra.Tridiagonal}) = 2
 ndims(::Type{<:WrappedArray{<:Any,N}}) where {N} = N
 
 eltype(::Type{<:WrappedArray{T}}) where {T} = T  # every wrapper has a T typevar
 
 for T in [:(Base.LogicalIndex{<:Any,<:Src}),
           :(PermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:Src}),
-          :(Adjoint{<:Any,<:Src}),
-          :(Transpose{<:Any,<:Src}),
-          :(Diagonal{<:Any,<:Src}),
-          :(Bidiagonal{<:Any,<:Src}),
-          :(Tridiagonal{<:Any,<:Src}),
-          :(SymTridiagonal{<:Any,<:Src}),
           :(WrappedReinterpretArray{<:Any,<:Any,<:Src}),
           :(WrappedReshapedArray{<:Any,<:Any,<:Src}),
           :(WrappedSubArray{<:Any,<:Any,<:Src})]
diff --git a/test/runtests.jl b/test/runtests.jl
index 7534635..11b4a6e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -41,9 +41,7 @@ macro test_adapt(to, src_expr, dst_expr, typ=nothing)
     end
 end
 
-AnyCustomArray{T,N} = Union{CustomArray{T,N},WrappedArray{T,N,CustomArray,CustomArray{T,N}}}
-AnyCustomVector{T} = AnyCustomArray{T,1}
-AnyCustomMatrix{T} = AnyCustomArray{T,2}
+AnyCustomArray{T,N} = Union{CustomArray,WrappedArray{T,N,CustomArray,CustomArray{T,N}}}
 
 
 # basic adaption
@@ -130,82 +128,75 @@ end
 
 @testset "array wrappers" begin
 
-@test_adapt CustomArray view(mat.arr,:,:) view(mat,:,:) AnyCustomMatrix
+@test_adapt CustomArray view(mat.arr,:,:) view(mat,:,:) AnyCustomArray
 inds = CustomArray{Int,1}([1,2])
-@test_adapt CustomArray view(mat.arr,inds.arr,:) view(mat,inds,:) AnyCustomMatrix
+@test_adapt CustomArray view(mat.arr,inds.arr,:) view(mat,inds,:) AnyCustomArray
 
 # NOTE: manual creation of PermutedDimsArray because permutedims collects
-@test_adapt CustomArray PermutedDimsArray(mat.arr,(2,1)) PermutedDimsArray(mat,(2,1)) AnyCustomMatrix
+@test_adapt CustomArray PermutedDimsArray(mat.arr,(2,1)) PermutedDimsArray(mat,(2,1)) AnyCustomArray
 
 # NOTE: manual creation of ReshapedArray because Base.Array has an optimized `reshape`
-@test_adapt CustomArray Base.ReshapedArray(mat.arr,(2,2),()) reshape(mat,(2,2)) AnyCustomMatrix
+@test_adapt CustomArray Base.ReshapedArray(mat.arr,(2,2),()) reshape(mat,(2,2)) AnyCustomArray
 
-@test_adapt CustomArray Base.LogicalIndex(mat_bools.arr) Base.LogicalIndex(mat_bools) AnyCustomVector
+@test_adapt CustomArray Base.LogicalIndex(mat_bools.arr) Base.LogicalIndex(mat_bools) AnyCustomArray
 
-@test_adapt CustomArray reinterpret(Int64,mat.arr) reinterpret(Int64,mat) AnyCustomMatrix
+@test_adapt CustomArray reinterpret(Int64,mat.arr) reinterpret(Int64,mat) AnyCustomArray
 
 @static if isdefined(Base, :NonReshapedReinterpretArray)
-    @test_adapt CustomArray reinterpret(reshape,Int64,mat.arr) reinterpret(reshape,Int64,mat) AnyCustomMatrix
+    @test_adapt CustomArray reinterpret(reshape,Int64,mat.arr) reinterpret(reshape,Int64,mat) AnyCustomArray
 end
 
 
 ## doubly-wrapped
 
-@test_adapt CustomArray reinterpret(Int64,view(mat.arr,:,:)) reinterpret(Int64,view(mat,:,:)) AnyCustomMatrix
+@test_adapt CustomArray reinterpret(Int64,view(mat.arr,:,:)) reinterpret(Int64,view(mat,:,:)) AnyCustomArray
 
-@test_adapt CustomArray reshape(view(mat.arr,:,:), (2,2)) reshape(view(mat,:,:), (2,2)) AnyCustomMatrix
-@test_adapt CustomArray reshape(reinterpret(Int64,mat.arr), (2,2)) reshape(reinterpret(Int64,mat), (2,2)) AnyCustomMatrix
-@test_adapt CustomArray reshape(reinterpret(Int64,view(mat.arr,:,:)), (2,2)) reshape(reinterpret(Int64,view(mat,:,:)), (2,2)) AnyCustomMatrix
+@test_adapt CustomArray reshape(view(mat.arr,:,:), (2,2)) reshape(view(mat,:,:), (2,2)) AnyCustomArray
+@test_adapt CustomArray reshape(reinterpret(Int64,mat.arr), (2,2)) reshape(reinterpret(Int64,mat), (2,2)) AnyCustomArray
+@test_adapt CustomArray reshape(reinterpret(Int64,view(mat.arr,:,:)), (2,2)) reshape(reinterpret(Int64,view(mat,:,:)), (2,2)) AnyCustomArray
 
-@test_adapt CustomArray view(reinterpret(Int64,mat.arr), :, :) view(reinterpret(Int64,mat), :, :) AnyCustomMatrix
-@test_adapt CustomArray view(reinterpret(Int64,view(mat.arr,:,:)), :, :) view(reinterpret(Int64,view(mat,:,:)), :, :) AnyCustomMatrix
-@test_adapt CustomArray view(Base.ReshapedArray(mat.arr,(2,2),()), :, :) view(reshape(mat, (2,2)), :, :) AnyCustomMatrix
-@test_adapt CustomArray view(reshape(view(mat.arr,:,:), (2,2)), :, :) view(reshape(view(mat,:,:), (2,2)), :, :) AnyCustomMatrix
-@test_adapt CustomArray view(reshape(reinterpret(Int64,mat.arr), (2,2)), :, :) view(reshape(reinterpret(Int64,mat), (2,2)), :, :) AnyCustomMatrix
-@test_adapt CustomArray view(reshape(reinterpret(Int64,view(mat.arr,:,:)), (2,2)), :, :) view(reshape(reinterpret(Int64,view(mat,:,:)), (2,2)), :, :) AnyCustomMatrix
+@test_adapt CustomArray view(reinterpret(Int64,mat.arr), :, :) view(reinterpret(Int64,mat), :, :) AnyCustomArray
+@test_adapt CustomArray view(reinterpret(Int64,view(mat.arr,:,:)), :, :) view(reinterpret(Int64,view(mat,:,:)), :, :) AnyCustomArray
+@test_adapt CustomArray view(Base.ReshapedArray(mat.arr,(2,2),()), :, :) view(reshape(mat, (2,2)), :, :) AnyCustomArray
+@test_adapt CustomArray view(reshape(view(mat.arr,:,:), (2,2)), :, :) view(reshape(view(mat,:,:), (2,2)), :, :) AnyCustomArray
+@test_adapt CustomArray view(reshape(reinterpret(Int64,mat.arr), (2,2)), :, :) view(reshape(reinterpret(Int64,mat), (2,2)), :, :) AnyCustomArray
+@test_adapt CustomArray view(reshape(reinterpret(Int64,view(mat.arr,:,:)), (2,2)), :, :) view(reshape(reinterpret(Int64,view(mat,:,:)), (2,2)), :, :) AnyCustomArray
 
 @static if isdefined(Base, :NonReshapedReinterpretArray)
-    @test_adapt CustomArray reinterpret(reshape,Int64,view(mat.arr,:,:)) reinterpret(reshape,Int64,view(mat,:,:)) AnyCustomMatrix
-    @test_adapt CustomArray view(reinterpret(reshape,Int64,mat.arr), :, :) view(reinterpret(reshape,Int64,mat), :, :) AnyCustomMatrix
-    @test_adapt CustomArray view(reinterpret(reshape,Int64,view(mat.arr,:,:)), :, :) view(reinterpret(reshape,Int64,view(mat,:,:)), :, :) AnyCustomMatrix
+    @test_adapt CustomArray reinterpret(reshape,Int64,view(mat.arr,:,:)) reinterpret(reshape,Int64,view(mat,:,:)) AnyCustomArray
+    @test_adapt CustomArray view(reinterpret(reshape,Int64,mat.arr), :, :) view(reinterpret(reshape,Int64,mat), :, :) AnyCustomArray
+    @test_adapt CustomArray view(reinterpret(reshape,Int64,view(mat.arr,:,:)), :, :) view(reinterpret(reshape,Int64,view(mat,:,:)), :, :) AnyCustomArray
 end
 
 
 using LinearAlgebra
 
-@test_adapt CustomArray mat.arr' mat' AnyCustomMatrix
+@test_adapt CustomArray mat.arr' mat' AnyCustomArray
 
-@test_adapt CustomArray transpose(mat.arr) transpose(mat) AnyCustomMatrix
+@test_adapt CustomArray transpose(mat.arr) transpose(mat) AnyCustomArray
 
-@test_adapt CustomArray LowerTriangular(mat.arr) LowerTriangular(mat) AnyCustomMatrix
-@test_adapt CustomArray UnitLowerTriangular(mat.arr) UnitLowerTriangular(mat) AnyCustomMatrix
-@test_adapt CustomArray UpperTriangular(mat.arr) UpperTriangular(mat) AnyCustomMatrix
-@test_adapt CustomArray UnitUpperTriangular(mat.arr) UnitUpperTriangular(mat) AnyCustomMatrix
-@test_adapt CustomArray Symmetric(mat.arr, :U) Symmetric(mat, :U) AnyCustomMatrix
-@test_adapt CustomArray Symmetric(mat.arr, :L) Symmetric(mat, :L) AnyCustomMatrix
-@test_adapt CustomArray Hermitian(mat.arr, :U) Hermitian(mat, :U) AnyCustomMatrix
-@test_adapt CustomArray Hermitian(mat.arr, :L) Hermitian(mat, :L) AnyCustomMatrix
-@test_adapt CustomArray UpperHessenberg(mat.arr) UpperHessenberg(mat) AnyCustomMatrix
+@test_adapt CustomArray LowerTriangular(mat.arr) LowerTriangular(mat) AnyCustomArray
+@test_adapt CustomArray UnitLowerTriangular(mat.arr) UnitLowerTriangular(mat) AnyCustomArray
+@test_adapt CustomArray UpperTriangular(mat.arr) UpperTriangular(mat) AnyCustomArray
+@test_adapt CustomArray UnitUpperTriangular(mat.arr) UnitUpperTriangular(mat) AnyCustomArray
+@test_adapt CustomArray Symmetric(mat.arr) Symmetric(mat) AnyCustomArray
 
-@test_adapt CustomArray Diagonal(vec.arr) Diagonal(vec) AnyCustomMatrix
+@test_adapt CustomArray Diagonal(vec.arr) Diagonal(vec) AnyCustomArray
 
 dl = CustomArray{Float64,1}(rand(2))
 du = CustomArray{Float64,1}(rand(2))
 d = CustomArray{Float64,1}(rand(3))
-@test_adapt CustomArray Bidiagonal(d.arr, du.arr, :U) Bidiagonal(d, du, :U) AnyCustomMatrix
-@test_adapt CustomArray Bidiagonal(d.arr, dl.arr, :L) Bidiagonal(d, dl, :L) AnyCustomMatrix
-@test_adapt CustomArray Tridiagonal(dl.arr, d.arr, du.arr) Tridiagonal(dl, d, du) AnyCustomMatrix
-@test_adapt CustomArray SymTridiagonal(d.arr, du.arr) SymTridiagonal(d, du) AnyCustomMatrix
+@test_adapt CustomArray Tridiagonal(dl.arr, d.arr, du.arr) Tridiagonal(dl, d, du) AnyCustomArray
 
 end
 
 
 @testset "type information" begin
-    @test Adapt.ndims(Transpose{Float64,Array{Float64,1}}) == 2
-    @test Adapt.ndims(Adapt.WrappedSubArray{Float64,3,Array{Float64,4}}) == 3
+    @test Adapt.ndims(LinearAlgebra.Transpose{Float64,Array{Float64,1}}) == 2
+    @test Adapt.ndims(Adapt.WrappedSubArray{Float64,3,Array{Float64,3}}) == 3
 
-    @test Adapt.parent(Transpose{Float64,Array{Float64,1}}) == Array
-    @test Adapt.parent(Adapt.WrappedSubArray{Float64,3,Array{Float64,4}}) == Array
+    @test Adapt.parent(LinearAlgebra.Transpose{Float64,Array{Float64,1}}) == Array
+    @test Adapt.parent(Adapt.WrappedSubArray{Float64,3,Array{Float64,3}}) == Array
 end