diff --git a/Project.toml b/Project.toml
index 17a1cbe..be0ea81 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,9 +1,16 @@
 name = "FunctionImplementations"
 uuid = "7c7cc465-9c6a-495f-bdd1-f42428e86d0c"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.2.0"
+version = "0.2.1"
+
+[weakdeps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[extensions]
+FunctionImplementationsLinearAlgebraExt = "LinearAlgebra"
 
 [compat]
+LinearAlgebra = "1.10"
 julia = "1.10"
 
 [workspace]
diff --git a/ext/FunctionImplementationsLinearAlgebraExt/FunctionImplementationsLinearAlgebraExt.jl b/ext/FunctionImplementationsLinearAlgebraExt/FunctionImplementationsLinearAlgebraExt.jl
new file mode 100644
index 0000000..6182553
--- /dev/null
+++ b/ext/FunctionImplementationsLinearAlgebraExt/FunctionImplementationsLinearAlgebraExt.jl
@@ -0,0 +1,15 @@
+module FunctionImplementationsLinearAlgebraExt
+
+import FunctionImplementations as FI
+import LinearAlgebra as LA
+
+struct DiagonalStyle <: FI.AbstractMatrixStyle end
+FI.Style(::Type{<:LA.Diagonal}) = DiagonalStyle()
+const permuteddims_diag = DiagonalStyle()(FI.permuteddims)
+function permuteddims_diag(a::AbstractArray, perm)
+    (ndims(a) == length(perm) && isperm(perm)) ||
+        throw(ArgumentError("no valid permutation of dimensions"))
+    return a
+end
+
+end
diff --git a/src/FunctionImplementations.jl b/src/FunctionImplementations.jl
index 186c693..5581f9e 100644
--- a/src/FunctionImplementations.jl
+++ b/src/FunctionImplementations.jl
@@ -2,5 +2,6 @@ module FunctionImplementations
 
 include("implementation.jl")
 include("style.jl")
+include("permuteddims.jl")
 
 end
diff --git a/src/permuteddims.jl b/src/permuteddims.jl
new file mode 100644
index 0000000..95758a9
--- /dev/null
+++ b/src/permuteddims.jl
@@ -0,0 +1,11 @@
+# See: https://github.com/JuliaLang/julia/issues/53188
+"""
+    permuteddims(a::AbstractArray, perm)
+
+Lazy version of `permutedims`. Defaults to constructing a `Base.PermutedDimsArray`
+but can be customized to output a different type of array.
+"""
+permuteddims(a::AbstractArray, perm) = style(a)(permuteddims)(a, perm)
+function (::Implementation{typeof(permuteddims)})(a::AbstractArray, perm)
+    return PermutedDimsArray(a, perm)
+end
diff --git a/src/style.jl b/src/style.jl
index 8324030..c05eefd 100644
--- a/src/style.jl
+++ b/src/style.jl
@@ -54,6 +54,8 @@ define binary [`Style`](@ref) rules to control the output type.
 See also [`FunctionImplementations.DefaultArrayStyle`](@ref).
 """
 abstract type AbstractArrayStyle{N} <: Style end
+abstract type AbstractVectorStyle <: AbstractArrayStyle{1} end
+abstract type AbstractMatrixStyle <: AbstractArrayStyle{2} end
 
 """
 `FunctionImplementations.DefaultArrayStyle{N}()` is a [`FunctionImplementations.Style`](@ref) indicating that an object
diff --git a/test/Project.toml b/test/Project.toml
index 8f9d369..00f25b1 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,6 +1,7 @@
 [deps]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 FunctionImplementations = "7c7cc465-9c6a-495f-bdd1-f42428e86d0c"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
@@ -11,6 +12,7 @@ FunctionImplementations = {path = ".."}
 [compat]
 Aqua = "0.8"
 FunctionImplementations = "0.2"
+LinearAlgebra = "1.10"
 SafeTestsets = "0.1"
 Suppressor = "0.2"
 Test = "1.10"
diff --git a/test/test_permuteddims.jl b/test/test_permuteddims.jl
new file mode 100644
index 0000000..14b0480
--- /dev/null
+++ b/test/test_permuteddims.jl
@@ -0,0 +1,18 @@
+import FunctionImplementations as FI
+import LinearAlgebra as LA
+using Test: @test, @testset
+
+@testset "permuteddims" begin
+    @testset "Array" begin
+        a = randn(2, 3)
+        b = FI.permuteddims(a, (2, 1))
+        @test b ≡ PermutedDimsArray(a, (2, 1))
+        @test size(b) == (3, 2)
+        @test b == permutedims(a, (2, 1))
+    end
+    @testset "Diagonal" begin
+        a = LA.Diagonal(randn(3))
+        b = FI.permuteddims(a, (2, 1))
+        @test b ≡ a
+    end
+end