diff --git a/Project.toml b/Project.toml
index fd11f26..7327e3b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,15 +1,23 @@
 name = "SerializedArrays"
 uuid = "621c0da3-e96e-4f80-bd06-5ae31cdfcb39"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.1.0"
+version = "0.1.1"
 
 [deps]
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DiskArrays = "3c3547ce-8d99-4f5e-a174-61eb10b00ae3"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
+[weakdeps]
+Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[extensions]
+SerializedArraysAdaptExt = "Adapt"
+SerializedArraysLinearAlgebraExt = "LinearAlgebra"
+
 [compat]
+Adapt = "4.3.0"
 ConstructionBase = "1.5.8"
 DiskArrays = "0.4.12"
 LinearAlgebra = "1.10"
diff --git a/ext/SerializedArraysAdaptExt/SerializedArraysAdaptExt.jl b/ext/SerializedArraysAdaptExt/SerializedArraysAdaptExt.jl
new file mode 100644
index 0000000..8dbc07b
--- /dev/null
+++ b/ext/SerializedArraysAdaptExt/SerializedArraysAdaptExt.jl
@@ -0,0 +1,10 @@
+module SerializedArraysAdaptExt
+
+using Adapt: Adapt
+using SerializedArrays: SerializedArray
+
+function Adapt.adapt_storage(arrayt::Type{<:SerializedArray}, a::AbstractArray)
+  return convert(arrayt, a)
+end
+
+end
diff --git a/ext/SerializedArraysLinearAlgebraExt/SerializedArraysLinearAlgebraExt.jl b/ext/SerializedArraysLinearAlgebraExt/SerializedArraysLinearAlgebraExt.jl
new file mode 100644
index 0000000..d28d8e7
--- /dev/null
+++ b/ext/SerializedArraysLinearAlgebraExt/SerializedArraysLinearAlgebraExt.jl
@@ -0,0 +1,25 @@
+module SerializedArraysLinearAlgebraExt
+
+using LinearAlgebra: LinearAlgebra, mul!
+using SerializedArrays: AbstractSerializedMatrix
+
+function LinearAlgebra.mul!(
+  a_dest::AbstractMatrix,
+  a1::AbstractSerializedMatrix,
+  a2::AbstractSerializedMatrix,
+  α::Number,
+  β::Number,
+)
+  mul!(a_dest, copy(a1), copy(a2), α, β)
+  return a_dest
+end
+
+for f in [:eigen, :qr, :svd]
+  @eval begin
+    function LinearAlgebra.$f(a::AbstractSerializedMatrix; kwargs...)
+      return LinearAlgebra.$f(copy(a))
+    end
+  end
+end
+
+end
diff --git a/src/SerializedArrays.jl b/src/SerializedArrays.jl
index b888e25..b931ca9 100644
--- a/src/SerializedArrays.jl
+++ b/src/SerializedArrays.jl
@@ -1,11 +1,69 @@
 module SerializedArrays
 
+using Base.PermutedDimsArrays: genperm
 using ConstructionBase: constructorof
-using DiskArrays: DiskArrays, AbstractDiskArray, Unchunked
-using LinearAlgebra: LinearAlgebra, mul!
+using DiskArrays: DiskArrays, AbstractDiskArray, Unchunked, readblock!, writeblock!
 using Serialization: deserialize, serialize
 
-struct SerializedArray{T,N,A<:AbstractArray{T,N},Axes} <: AbstractDiskArray{T,N}
+abstract type AbstractSerializedArray{T,N} <: AbstractDiskArray{T,N} end
+const AbstractSerializedMatrix{T} = AbstractSerializedArray{T,2}
+const AbstractSerializedVector{T} = AbstractSerializedArray{T,1}
+
+function _copyto_write!(dst, src)
+  writeblock!(dst, src, axes(src)...)
+  return dst
+end
+function _copyto_read!(dst, src)
+  readblock!(src, dst, axes(src)...)
+  return dst
+end
+
+function Base.copyto!(dst::AbstractSerializedArray, src::AbstractArray)
+  return _copyto_write!(dst, src)
+end
+function Base.copyto!(dst::AbstractArray, src::AbstractSerializedArray)
+  return _copyto_read!(dst, src)
+end
+# Fix ambiguity error.
+function Base.copyto!(dst::AbstractSerializedArray, src::AbstractSerializedArray)
+  return copyto!(dst, copy(src))
+end
+# Fix ambiguity error.
+function Base.copyto!(dst::AbstractDiskArray, src::AbstractSerializedArray)
+  return copyto!(dst, copy(src))
+end
+# Fix ambiguity error.
+function Base.copyto!(dst::AbstractSerializedArray, src::AbstractDiskArray)
+  return _copyto_write!(dst, src)
+end
+# Fix ambiguity error.
+function Base.copyto!(dst::PermutedDimsArray, src::AbstractSerializedArray)
+  return _copyto_read!(dst, src)
+end
+
+function Base.:(==)(a1::AbstractSerializedArray, a2::AbstractSerializedArray)
+  return copy(a1) == copy(a2)
+end
+function Base.:(==)(a1::AbstractArray, a2::AbstractSerializedArray)
+  return a1 == copy(a2)
+end
+function Base.:(==)(a1::AbstractSerializedArray, a2::AbstractArray)
+  return copy(a1) == a2
+end
+
+# # These cause too many ambiguity errors, try bringing them back.
+# function Base.convert(arrayt::Type{<:AbstractSerializedArray}, a::AbstractArray)
+#   return arrayt(a)
+# end
+# function Base.convert(arrayt::Type{<:AbstractArray}, a::AbstractSerializedArray)
+#   return convert(arrayt, copy(a))
+# end
+# # Fixes ambiguity error.
+# function Base.convert(arrayt::Type{<:Array}, a::AbstractSerializedArray)
+#   return convert(arrayt, copy(a))
+# end
+
+struct SerializedArray{T,N,A<:AbstractArray{T,N},Axes} <: AbstractSerializedArray{T,N}
   file::String
   axes::Axes
 end
@@ -22,17 +80,26 @@ function SerializedArray(a::AbstractArray)
   return SerializedArray(tempname(), a)
 end
 
+function Base.convert(arrayt::Type{<:SerializedArray}, a::AbstractArray)
+  return arrayt(a)
+end
+
 function Base.similar(a::SerializedArray, elt::Type, dims::Tuple{Vararg{Int}})
   return constructorof(arraytype(a)){elt}(undef, dims...)
 end
 
+function materialize(a::SerializedArray)
+  return deserialize(file(a))::arraytype(a)
+end
 function Base.copy(a::SerializedArray)
-  arrayt = arraytype(a)
-  return convert(arrayt, deserialize(file(a)))::arrayt
+  return materialize(a)
 end
 
 Base.size(a::SerializedArray) = length.(axes(a))
 
+to_axis(r::AbstractUnitRange) = r
+to_axis(d::Integer) = Base.OneTo(d)
+
 #
 # DiskArrays
 #
@@ -64,6 +131,131 @@ function DiskArrays.create_outputarray(::Nothing, a::SerializedArray, output_siz
   return similar(a, output_size)
 end
 
+struct PermutedSerializedArray{T,N,P<:PermutedDimsArray{T,N}} <:
+       AbstractSerializedArray{T,N}
+  permuted_parent::P
+end
+Base.parent(a::PermutedSerializedArray) = parent(getfield(a, :permuted_parent))
+
+perm(a::PermutedSerializedArray) = perm(a.permuted_parent)
+perm(::PermutedDimsArray{<:Any,<:Any,p}) where {p} = p
+
+iperm(a::PermutedSerializedArray) = iperm(a.permuted_parent)
+iperm(::PermutedDimsArray{<:Any,<:Any,<:Any,ip}) where {ip} = ip
+
+Base.axes(a::PermutedSerializedArray) = genperm(axes(parent(a)), perm(a))
+Base.size(a::PermutedSerializedArray) = length.(axes(a))
+
+function PermutedSerializedArray(a::AbstractArray, perm)
+  a′ = PermutedDimsArray(a, perm)
+  return PermutedSerializedArray{eltype(a),ndims(a),typeof(a′)}(a′)
+end
+
+function Base.permutedims(a::AbstractSerializedArray, perm)
+  return PermutedSerializedArray(a, perm)
+end
+
+function Base.similar(a::PermutedSerializedArray, elt::Type, dims::Tuple{Vararg{Int}})
+  return similar(parent(a), elt, dims)
+end
+
+function materialize(a::PermutedSerializedArray)
+  return PermutedDimsArray(copy(parent(a)), perm(a))
+end
+function Base.copy(a::PermutedSerializedArray)
+  return copy(materialize(a))
+end
+
+haschunks(a::PermutedSerializedArray) = Unchunked()
+function DiskArrays.readblock!(a::PermutedSerializedArray, aout, i::OrdinalRange...)
+  ip = iperm(a)
+  # Permute the indices
+  inew = genperm(i, ip)
+  # Permute the dest block and read from the true parent
+  DiskArrays.readblock!(parent(a), PermutedDimsArray(aout, ip), inew...)
+  return nothing
+end
+function DiskArrays.writeblock!(a::PermutedSerializedArray, v, i::OrdinalRange...)
+  ip = iperm(a)
+  inew = genperm(i, ip)
+  # Permute the dest block and write from the true parent
+  DiskArrays.writeblock!(parent(a), PermutedDimsArray(v, ip), inew...)
+  return nothing
+end
+
+struct ReshapedSerializedArray{T,N,P<:AbstractArray{T},Axes} <: AbstractSerializedArray{T,N}
+  parent::P
+  axes::Axes
+end
+Base.parent(a::ReshapedSerializedArray) = getfield(a, :parent)
+Base.axes(a::ReshapedSerializedArray) = getfield(a, :axes)
+
+function ReshapedSerializedArray(
+  a::AbstractSerializedArray,
+  ax::Tuple{AbstractUnitRange{<:Integer},Vararg{AbstractUnitRange{<:Integer}}},
+)
+  return ReshapedSerializedArray{eltype(a),length(ax),typeof(a),typeof(ax)}(a, ax)
+end
+function ReshapedSerializedArray(
+  a::AbstractSerializedArray,
+  shape::Tuple{
+    Union{Integer,AbstractUnitRange{<:Integer}},
+    Vararg{Union{Integer,AbstractUnitRange{<:Integer}}},
+  },
+)
+  return ReshapedSerializedArray(a, to_axis.(shape))
+end
+
+Base.size(a::ReshapedSerializedArray) = length.(axes(a))
+
+function Base.similar(a::ReshapedSerializedArray, elt::Type, dims::Tuple{Vararg{Int}})
+  return similar(parent(a), elt, dims)
+end
+
+function materialize(a::ReshapedSerializedArray)
+  return reshape(materialize(parent(a)), axes(a))
+end
+function Base.copy(a::ReshapedSerializedArray)
+  a′ = materialize(a)
+  return a′ isa Base.ReshapedArray ? copy(a′) : a′
+end
+
+# Special case for handling nested wrappers that aren't
+# friendly on GPU. Consider special cases of strded arrays
+# and handle with stride manipulations.
+function Base.copy(a::ReshapedSerializedArray{<:Any,<:Any,<:PermutedSerializedArray})
+  a′ = reshape(copy(parent(a)), axes(a))
+  return a′ isa Base.ReshapedArray ? copy(a′) : a′
+end
+
+function Base.reshape(a::AbstractSerializedArray, dims::Tuple{Int,Vararg{Int}})
+  return ReshapedSerializedArray(a, dims)
+end
+
+DiskArrays.haschunks(a::ReshapedSerializedArray) = Unchunked()
+function DiskArrays.readblock!(
+  a::ReshapedSerializedArray{<:Any,N}, aout, i::Vararg{AbstractUnitRange,N}
+) where {N}
+  if i == axes(a)
+    aout .= copy(a)
+    return a
+  end
+  aout .= @view copy(a)[i...]
+  return nothing
+end
+function DiskArrays.writeblock!(
+  a::ReshapedSerializedArray{<:Any,N}, ain, i::Vararg{AbstractUnitRange,N}
+) where {N}
+  if i == axes(a)
+    serialize(file(a), ain)
+    return a
+  end
+  a′ = copy(a)
+  a′[i...] = ain
+  serialize(file(a), a′)
+  return nothing
+end
+
 #
 # Broadcast
 #
@@ -86,7 +278,7 @@ function Base.BroadcastStyle(::DefaultArrayStyle{M}, ::SerializedArrayStyle{N})
 end
 
 struct BroadcastSerializedArray{T,N,BC<:Broadcasted{<:SerializedArrayStyle{N}}} <:
-       AbstractDiskArray{T,N}
+       AbstractSerializedArray{T,N}
   broadcasted::BC
 end
 function BroadcastSerializedArray(
@@ -106,15 +298,4 @@ function Base.copy(broadcasted::Broadcasted{SerializedArrayStyle{N}}) where {N}
   return BroadcastSerializedArray(flatten(broadcasted))
 end
 
-#
-# LinearAlgebra
-#
-
-function LinearAlgebra.mul!(
-  a_dest::AbstractMatrix, a1::SerializedArray, a2::SerializedArray, α::Number, β::Number
-)
-  mul!(a_dest, copy(a1), copy(a2), α, β)
-  return a_dest
-end
-
 end
diff --git a/test/Project.toml b/test/Project.toml
index 3064946..d9107f5 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,7 +1,9 @@
 [deps]
+Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
 JLArrays = "27aeb0d3-9eb9-45fb-866b-73c2ecf80fcb"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SerializedArrays = "621c0da3-e96e-4f80-bd06-5ae31cdfcb39"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
@@ -10,9 +12,11 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestExtras = "5ed8adda-3752-4e41-b88a-e8b09835ee3a"
 
 [compat]
+Adapt = "4"
 Aqua = "0.8"
 GPUArraysCore = "0.2"
 JLArrays = "0.2"
+LinearAlgebra = "1.10"
 SafeTestsets = "0.1"
 SerializedArrays = "0.1"
 StableRNGs = "1"
diff --git a/test/test_adaptext.jl b/test/test_adaptext.jl
new file mode 100644
index 0000000..5f461ae
--- /dev/null
+++ b/test/test_adaptext.jl
@@ -0,0 +1,22 @@
+using Adapt: adapt
+using JLArrays: JLArray
+using SerializedArrays: SerializedArray
+using StableRNGs: StableRNG
+using Test: @test, @testset
+using TestExtras: @constinferred
+
+elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
+arrayts = (Array, JLArray)
+@testset "SerializedArraysAdaptExt (eltype=$elt, arraytype=$arrayt)" for elt in elts,
+  arrayt in arrayts
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  y = PermutedDimsArray(x, (2, 1))
+  a = adapt(SerializedArray, x)
+  @test a isa SerializedArray{elt,2,arrayt{elt,2}}
+  b = adapt(SerializedArray, y)
+  @test b isa
+    PermutedDimsArray{elt,2,(2, 1),(2, 1),<:SerializedArray{elt,2,<:arrayt{elt,2}}}
+  @test parent(b) == a
+end
diff --git a/test/test_basics.jl b/test/test_basics.jl
index 5bc6690..a4269be 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -1,6 +1,6 @@
 using GPUArraysCore: @allowscalar
 using JLArrays: JLArray
-using SerializedArrays: SerializedArray
+using SerializedArrays: PermutedSerializedArray, ReshapedSerializedArray, SerializedArray
 using StableRNGs: StableRNG
 using Test: @test, @testset
 using TestExtras: @constinferred
@@ -36,4 +36,64 @@ arrayts = (Array, JLArray)
   c = @constinferred(a * b)
   @test c == x * y
   @test c isa arrayt{elt,2}
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  b = similar(a)
+  @test b isa arrayt{elt,2}
+  @test size(b) == size(a) == size(x)
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  a = permutedims(SerializedArray(x), (2, 1))
+  @test a isa PermutedSerializedArray{elt,2}
+  @test similar(a) isa arrayt{elt,2}
+  @test copy(a) == permutedims(x, (2, 1))
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  a = reshape(SerializedArray(x), 16)
+  @test a isa ReshapedSerializedArray{elt,1}
+  @test similar(a) isa arrayt{elt,1}
+  @test copy(a) == reshape(x, 16)
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  a = reshape(permutedims(SerializedArray(x), (2, 1)), 16)
+  @test a isa ReshapedSerializedArray{elt,1,<:PermutedSerializedArray{elt,2}}
+  @test similar(a) isa arrayt{elt,1}
+  @test copy(a) == reshape(permutedims(x, (2, 1)), 16)
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  @test a == a
+  @test x == a
+  @test a == x
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  y = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  b = SerializedArray(y)
+  copyto!(b, a)
+  @test b == a
+  @test b == x
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  y = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  b = SerializedArray(y)
+  copyto!(b, x)
+  @test b == a
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  y = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  copyto!(y, a)
+  b = SerializedArray(y)
+  @test b == a
 end
diff --git a/test/test_linearalgebraext.jl b/test/test_linearalgebraext.jl
new file mode 100644
index 0000000..2b5f769
--- /dev/null
+++ b/test/test_linearalgebraext.jl
@@ -0,0 +1,42 @@
+using JLArrays: JLArray
+using LinearAlgebra: eigen, qr, svd
+using SerializedArrays: SerializedArray
+using StableRNGs: StableRNG
+using Test: @test, @testset
+using TestExtras: @constinferred
+
+elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
+arrayts = (Array, JLArray)
+@testset "SerializedArraysLinearAlgebraExt (eltype=$elt, arraytype=$arrayt)" for elt in
+                                                                                 elts,
+  arrayt in arrayts
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  y = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  b = SerializedArray(y)
+  c = @constinferred(a * b)
+  @test c == x * y
+  @test c isa arrayt{elt,2}
+
+  a = permutedims(SerializedArray(x), (2, 1))
+  b = permutedims(SerializedArray(y), (2, 1))
+  c = @constinferred(a * b)
+  @test c == permutedims(x, (2, 1)) * permutedims(y, (2, 1))
+  @test c isa arrayt{elt,2}
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  # `LinearAlgebra.eigen(::JLArray)` is broken with
+  # a scalar indexing issue.
+  if arrayt ≠ JLArray
+    @test eigen(a) == eigen(x)
+  end
+  Q, R = qr(a)
+  Qₓ, Rₓ = qr(x)
+  @test Q == Qₓ
+  @test R == Rₓ
+  @test svd(a) == svd(x)
+end