diff --git a/Project.toml b/Project.toml
index 8da5421..38353b5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "KroneckerArrays"
 uuid = "05d0b138-81bc-4ff7-84be-08becefb1ccc"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.1.6"
+version = "0.1.7"
 
 [deps]
 DerivableInterfaces = "6c5e35bf-e59e-4898-b73c-732dcc4ba65f"
diff --git a/src/KroneckerArrays.jl b/src/KroneckerArrays.jl
index 3ae3fad..0bce6f8 100644
--- a/src/KroneckerArrays.jl
+++ b/src/KroneckerArrays.jl
@@ -11,6 +11,11 @@ end
 arguments(a::CartesianProduct) = (a.a, a.b)
 arguments(a::CartesianProduct, n::Int) = arguments(a)[n]
 
+function Base.show(io::IO, a::CartesianProduct)
+  print(io, a.a, " × ", a.b)
+  return nothing
+end
+
 ×(a, b) = CartesianProduct(a, b)
 Base.length(a::CartesianProduct) = length(a.a) * length(a.b)
 Base.getindex(a::CartesianProduct, i::CartesianProduct) = a.a[i.a] × a.b[i.b]
@@ -130,6 +135,8 @@ function interleave(x::Tuple, y::Tuple)
   xy = ntuple(i -> (x[i], y[i]), length(x))
   return flatten(xy)
 end
+# TODO: Maybe use scalar indexing based on KroneckerProducts.jl logic for cartesian indexing:
+# https://github.com/perrutquist/KroneckerProducts.jl/blob/8c0104caf1f17729eb067259ba1473986121d032/src/KroneckerProducts.jl#L59-L66
 function kron_nd(a::AbstractArray{<:Any,N}, b::AbstractArray{<:Any,N}) where {N}
   a′ = reshape(a, interleave(size(a), ntuple(one, N)))
   b′ = reshape(b, interleave(ntuple(one, N), size(b)))
@@ -183,6 +190,9 @@ function Base.getindex(a::KroneckerArray, i::Integer)
   return a[CartesianIndices(a)[i]]
 end
 
+# TODO: Use this logic from KroneckerProducts.jl for cartesian indexing
+# in the n-dimensional case and use it to replace the matrix and vector cases:
+# https://github.com/perrutquist/KroneckerProducts.jl/blob/8c0104caf1f17729eb067259ba1473986121d032/src/KroneckerProducts.jl#L59-L66
 function Base.getindex(a::KroneckerArray{<:Any,N}, I::Vararg{Integer,N}) where {N}
   return error("Not implemented.")
 end
@@ -222,6 +232,10 @@ end
 function Base.inv(a::KroneckerArray)
   return inv(a.a) ⊗ inv(a.b)
 end
+using LinearAlgebra: LinearAlgebra, pinv
+function LinearAlgebra.pinv(a::KroneckerArray; kwargs...)
+  return pinv(a.a; kwargs...) ⊗ pinv(a.b; kwargs...)
+end
 function Base.transpose(a::KroneckerArray)
   return transpose(a.a) ⊗ transpose(a.b)
 end
@@ -297,6 +311,7 @@ using LinearAlgebra:
   Diagonal,
   Eigen,
   SVD,
+  det,
   diag,
   eigen,
   eigvals,
@@ -335,9 +350,63 @@ end
 function LinearAlgebra.norm(a::KroneckerArray, p::Int=2)
   return norm(a.a, p) ⊗ norm(a.b, p)
 end
+
+using MatrixAlgebraKit: MatrixAlgebraKit, diagview
+function MatrixAlgebraKit.diagview(a::KroneckerMatrix)
+  return diagview(a.a) ⊗ diagview(a.b)
+end
 function LinearAlgebra.diag(a::KroneckerArray)
-  return diag(a.a) ⊗ diag(a.b)
+  return copy(diagview(a.a)) ⊗ copy(diagview(a.b))
+end
+
+# Matrix functions
+const MATRIX_FUNCTIONS = [
+  :exp,
+  :cis,
+  :log,
+  :sqrt,
+  :cbrt,
+  :cos,
+  :sin,
+  :tan,
+  :csc,
+  :sec,
+  :cot,
+  :cosh,
+  :sinh,
+  :tanh,
+  :csch,
+  :sech,
+  :coth,
+  :acos,
+  :asin,
+  :atan,
+  :acsc,
+  :asec,
+  :acot,
+  :acosh,
+  :asinh,
+  :atanh,
+  :acsch,
+  :asech,
+  :acoth,
+]
+
+for f in MATRIX_FUNCTIONS
+  @eval begin
+    function Base.$f(a::KroneckerArray)
+      return throw(ArgumentError("Generic KroneckerArray `$($f)` is not supported."))
+    end
+  end
+end
+
+using LinearAlgebra: checksquare
+function LinearAlgebra.det(a::KroneckerArray)
+  checksquare(a.a)
+  checksquare(a.b)
+  return det(a.a) ^ size(a.b, 1) * det(a.b) ^ size(a.a, 1)
 end
+
 function LinearAlgebra.svd(a::KroneckerArray)
   Fa = svd(a.a)
   Fb = svd(a.b)
@@ -690,18 +759,6 @@ for f in [:eig_vals!, :eigh_vals!, :svd_vals!]
   end
 end
 
-for f in [:eig_trunc!, :eigh_trunc!, :svd_trunc!]
-  @eval begin
-    function MatrixAlgebraKit.truncate!(
-      ::typeof($f),
-      (D, V)::Tuple{KroneckerMatrix,KroneckerMatrix},
-      strategy::TruncationStrategy,
-    )
-      return throw(MethodError(truncate!, ($f, (D, V), strategy)))
-    end
-  end
-end
-
 for f in [:left_orth!, :right_orth!]
   @eval begin
     function MatrixAlgebraKit.initialize_output(::typeof($f), a::KroneckerMatrix)
@@ -941,4 +998,110 @@ for f in [:eig_vals!, :eigh_vals!, :svd_vals!]
   end
 end
 
+using MatrixAlgebraKit: TruncationStrategy, diagview, findtruncated, truncate!
+
+struct KroneckerTruncationStrategy{T<:TruncationStrategy} <: TruncationStrategy
+  strategy::T
+end
+
+# Avoid instantiating the identity.
+function Base.getindex(a::SquareEyeKronecker, I::Vararg{CartesianProduct{Colon},2})
+  return a.a ⊗ a.b[I[1].b, I[2].b]
+end
+function Base.getindex(a::KroneckerSquareEye, I::Vararg{CartesianProduct{<:Any,Colon},2})
+  return a.a[I[1].a, I[2].a] ⊗ a.b
+end
+function Base.getindex(a::SquareEyeSquareEye, I::Vararg{CartesianProduct{Colon,Colon},2})
+  return a
+end
+
+using FillArrays: OnesVector
+const OnesKroneckerVector{T,A<:OnesVector{T},B<:AbstractVector{T}} = KroneckerVector{T,A,B}
+const KroneckerOnesVector{T,A<:AbstractVector{T},B<:OnesVector{T}} = KroneckerVector{T,A,B}
+const OnesVectorOnesVector{T,A<:OnesVector{T},B<:OnesVector{T}} = KroneckerVector{T,A,B}
+
+function MatrixAlgebraKit.findtruncated(
+  values::OnesKroneckerVector, strategy::KroneckerTruncationStrategy
+)
+  I = findtruncated(Vector(values), strategy.strategy)
+  prods = collect(only(axes(values)).product)[I]
+  I_data = unique(map(x -> x.a, prods))
+  # Drop truncations that occur within the identity.
+  I_data = filter(I_data) do i
+    return count(x -> x.a == i, prods) == length(values.a)
+  end
+  return (:) × I_data
+end
+function MatrixAlgebraKit.findtruncated(
+  values::KroneckerOnesVector, strategy::KroneckerTruncationStrategy
+)
+  I = findtruncated(Vector(values), strategy.strategy)
+  prods = collect(only(axes(values)).product)[I]
+  I_data = unique(map(x -> x.b, prods))
+  # Drop truncations that occur within the identity.
+  I_data = filter(I_data) do i
+    return count(x -> x.b == i, prods) == length(values.b)
+  end
+  return I_data × (:)
+end
+function MatrixAlgebraKit.findtruncated(
+  values::OnesVectorOnesVector, strategy::KroneckerTruncationStrategy
+)
+  return throw(ArgumentError("Can't truncate Eye ⊗ Eye."))
+end
+
+for f in [:eig_trunc!, :eigh_trunc!]
+  @eval begin
+    function MatrixAlgebraKit.truncate!(
+      ::typeof($f), DV::NTuple{2,KroneckerMatrix}, strategy::TruncationStrategy
+    )
+      return truncate!($f, DV, KroneckerTruncationStrategy(strategy))
+    end
+    function MatrixAlgebraKit.truncate!(
+      ::typeof($f), (D, V)::NTuple{2,KroneckerMatrix}, strategy::KroneckerTruncationStrategy
+    )
+      I = findtruncated(diagview(D), strategy)
+      return (D[I, I], V[(:) × (:), I])
+    end
+  end
+end
+
+function MatrixAlgebraKit.truncate!(
+  f::typeof(svd_trunc!), USVᴴ::NTuple{3,KroneckerMatrix}, strategy::TruncationStrategy
+)
+  return truncate!(f, USVᴴ, KroneckerTruncationStrategy(strategy))
+end
+function MatrixAlgebraKit.truncate!(
+  ::typeof(svd_trunc!),
+  (U, S, Vᴴ)::NTuple{3,KroneckerMatrix},
+  strategy::KroneckerTruncationStrategy,
+)
+  I = findtruncated(diagview(S), strategy)
+  return (U[(:) × (:), I], S[I, I], Vᴴ[I, (:) × (:)])
+end
+
+for f in MATRIX_FUNCTIONS
+  @eval begin
+    function Base.$f(a::SquareEyeKronecker)
+      return a.a ⊗ $f(a.b)
+    end
+    function Base.$f(a::KroneckerSquareEye)
+      return $f(a.a) ⊗ a.b
+    end
+    function Base.$f(a::SquareEyeSquareEye)
+      return throw(ArgumentError("`$($f)` on `Eye ⊗ Eye` is not supported."))
+    end
+  end
+end
+
+function LinearAlgebra.pinv(a::SquareEyeKronecker; kwargs...)
+  return a.a ⊗ pinv(a.b; kwargs...)
+end
+function LinearAlgebra.pinv(a::KroneckerSquareEye; kwargs...)
+  return pinv(a.a; kwargs...) ⊗ a.b
+end
+function LinearAlgebra.pinv(a::SquareEyeSquareEye; kwargs...)
+  return a
+end
+
 end
diff --git a/test/Project.toml b/test/Project.toml
index aebc8e9..7f96924 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -5,6 +5,7 @@ KroneckerArrays = "05d0b138-81bc-4ff7-84be-08becefb1ccc"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MatrixAlgebraKit = "6c742aac-3347-4629-af66-fc926824e5e4"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestExtras = "5ed8adda-3752-4e41-b88a-e8b09835ee3a"
@@ -16,6 +17,7 @@ KroneckerArrays = "0.1"
 LinearAlgebra = "1.10"
 MatrixAlgebraKit = "0.2"
 SafeTestsets = "0.1"
+StableRNGs = "1.0"
 Suppressor = "0.2"
 Test = "1.10"
 TestExtras = "0.3"
diff --git a/test/test_basics.jl b/test/test_basics.jl
index cb57239..c2aaedc 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -1,7 +1,8 @@
 using FillArrays: Eye
 using KroneckerArrays: KroneckerArrays, ⊗, ×, diagonal, kron_nd
-using LinearAlgebra: Diagonal, I, eigen, eigvals, lq, qr, svd, svdvals, tr
-using Test: @test, @testset
+using LinearAlgebra: Diagonal, I, det, eigen, eigvals, lq, pinv, qr, svd, svdvals, tr
+using StableRNGs: StableRNG
+using Test: @test, @test_broken, @test_throws, @testset
 
 const elts = (Float32, Float64, ComplexF32, ComplexF64)
 @testset "KroneckerArrays (eltype=$elt)" for elt in elts
@@ -35,7 +36,7 @@ const elts = (Float32, Float64, ComplexF32, ComplexF64)
   @test iszero(a - a)
   @test collect(a + c) ≈ collect(a) + collect(c)
   @test collect(b + c) ≈ collect(b) + collect(c)
-  for f in (transpose, adjoint, inv)
+  for f in (transpose, adjoint, inv, pinv)
     @test collect(f(a)) ≈ f(collect(a))
   end
   @test tr(a) ≈ tr(collect(a))
@@ -66,9 +67,25 @@ const elts = (Float32, Float64, ComplexF32, ComplexF64)
   Q, R = qr(a)
   @test collect(Q * R) ≈ collect(a)
   @test collect(Q'Q) ≈ I
+
+  a = randn(elt, 2, 2) ⊗ randn(elt, 3, 3)
+  @test det(a) ≈ det(collect(a))
+
+  a = randn(elt, 2, 2) ⊗ randn(elt, 3, 3)
+  for f in KroneckerArrays.MATRIX_FUNCTIONS
+    @eval begin
+      @test_throws ArgumentError $f($a)
+    end
+  end
 end
 
 @testset "FillArrays.Eye" begin
+  MATRIX_FUNCTIONS = KroneckerArrays.MATRIX_FUNCTIONS
+  if VERSION < v"1.11-"
+    # `cbrt(::AbstractMatrix{<:Real})` was implemented in Julia 1.11.
+    MATRIX_FUNCTIONS = setdiff(MATRIX_FUNCTIONS, [:cbrt])
+  end
+
   a = Eye(2) ⊗ randn(3, 3)
   @test size(a) == (6, 6)
   @test a + a == Eye(2) ⊗ (2a.b)
@@ -80,4 +97,66 @@ end
   @test a + a == (2a.a) ⊗ Eye(2)
   @test 2a == (2a.a) ⊗ Eye(2)
   @test a * a == (a.a * a.a) ⊗ Eye(2)
+
+  # Eye ⊗ A
+  rng = StableRNG(123)
+  a = Eye(2) ⊗ randn(rng, 3, 3)
+  for f in MATRIX_FUNCTIONS
+    @eval begin
+      fa = $f($a)
+      @test collect(fa) ≈ $f(collect($a)) rtol = ∜(eps(real(eltype($a))))
+      @test fa.a isa Eye
+    end
+  end
+
+  fa = inv(a)
+  @test collect(fa) ≈ inv(collect(a))
+  @test fa.a isa Eye
+
+  fa = pinv(a)
+  @test collect(fa) ≈ pinv(collect(a))
+  @test fa.a isa Eye
+
+  @test det(a) ≈ det(collect(a))
+
+  # A ⊗ Eye
+  rng = StableRNG(123)
+  a = randn(rng, 3, 3) ⊗ Eye(2)
+  for f in setdiff(MATRIX_FUNCTIONS, [:atanh])
+    @eval begin
+      fa = $f($a)
+      @test collect(fa) ≈ $f(collect($a)) rtol = ∜(eps(real(eltype($a))))
+      @test fa.b isa Eye
+    end
+  end
+
+  fa = inv(a)
+  @test collect(fa) ≈ inv(collect(a))
+  @test fa.b isa Eye
+
+  fa = pinv(a)
+  @test collect(fa) ≈ pinv(collect(a))
+  @test fa.b isa Eye
+
+  @test det(a) ≈ det(collect(a))
+
+  # Eye ⊗ Eye
+  a = Eye(2) ⊗ Eye(2)
+  for f in KroneckerArrays.MATRIX_FUNCTIONS
+    @eval begin
+      @test_throws ArgumentError $f($a)
+    end
+  end
+
+  fa = inv(a)
+  @test fa == a
+  @test fa.a isa Eye
+  @test fa.b isa Eye
+
+  fa = pinv(a)
+  @test fa == a
+  @test fa.a isa Eye
+  @test fa.b isa Eye
+
+  @test det(a) ≈ det(collect(a)) ≈ 1
 end
diff --git a/test/test_matrixalgebrakit.jl b/test/test_matrixalgebrakit.jl
index 82943cd..41983e5 100644
--- a/test/test_matrixalgebrakit.jl
+++ b/test/test_matrixalgebrakit.jl
@@ -121,12 +121,6 @@ herm(a) = parent(hermitianpart(a))
 end
 
 @testset "MatrixAlgebraKit + Eye" begin
-
-  # TODO:
-  # eig_trunc
-  # eigh_trunc
-  # svd_trunc
-
   for f in (eig_full, eigh_full)
     a = Eye(3) ⊗ parent(hermitianpart(randn(3, 3)))
     d, v = @constinferred f(a)
@@ -149,6 +143,27 @@ end
     @test arguments(v, 2) isa Eye
   end
 
+  for f in (eig_trunc, eigh_trunc)
+    a = Eye(3) ⊗ parent(hermitianpart(randn(3, 3)))
+    d, v = f(a; trunc=(; maxrank=7))
+    @test a * v ≈ v * d
+    @test arguments(d, 1) isa Eye
+    @test arguments(v, 1) isa Eye
+    @test size(d) == (6, 6)
+    @test size(v) == (9, 6)
+
+    a = parent(hermitianpart(randn(3, 3))) ⊗ Eye(3)
+    d, v = f(a; trunc=(; maxrank=7))
+    @test a * v ≈ v * d
+    @test arguments(d, 2) isa Eye
+    @test arguments(v, 2) isa Eye
+    @test size(d) == (6, 6)
+    @test size(v) == (9, 6)
+
+    a = Eye(3) ⊗ Eye(3)
+    @test_throws ArgumentError f(a)
+  end
+
   for f in (eig_vals, eigh_vals)
     a = Eye(3) ⊗ parent(hermitianpart(randn(3, 3)))
     d = @constinferred f(a)
@@ -221,6 +236,33 @@ end
     @test arguments(v, 2) isa Eye
   end
 
+  # svd_trunc
+  a = Eye(3) ⊗ randn(3, 3)
+  u, s, v = svd_trunc(a; trunc=(; maxrank=7))
+  u′, s′, v′ = svd_trunc(Matrix(a); trunc=(; maxrank=6))
+  @test Matrix(u * s * v) ≈ u′ * s′ * v′
+  @test arguments(u, 1) isa Eye
+  @test arguments(s, 1) isa Eye
+  @test arguments(v, 1) isa Eye
+  @test size(u) == (9, 6)
+  @test size(s) == (6, 6)
+  @test size(v) == (6, 9)
+
+  a = randn(3, 3) ⊗ Eye(3)
+  u, s, v = svd_trunc(a; trunc=(; maxrank=7))
+  u′, s′, v′ = svd_trunc(Matrix(a); trunc=(; maxrank=6))
+  @test Matrix(u * s * v) ≈ u′ * s′ * v′
+  @test arguments(u, 2) isa Eye
+  @test arguments(s, 2) isa Eye
+  @test arguments(v, 2) isa Eye
+  @test size(u) == (9, 6)
+  @test size(s) == (6, 6)
+  @test size(v) == (6, 9)
+
+  a = Eye(3) ⊗ Eye(3)
+  @test_throws ArgumentError svd_trunc(a)
+
+  # svd_vals
   a = Eye(3) ⊗ randn(3, 3)
   d = @constinferred svd_vals(a)
   d′ = svd_vals(Matrix(a))