diff --git a/Project.toml b/Project.toml
index f0ba43d..b0cf377 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 = "0.1.2"
+version = "0.1.3"
 
 [deps]
 DerivableInterfaces = "6c5e35bf-e59e-4898-b73c-732dcc4ba65f"
diff --git a/src/KroneckerArrays.jl b/src/KroneckerArrays.jl
index c072dbe..c910c7d 100644
--- a/src/KroneckerArrays.jl
+++ b/src/KroneckerArrays.jl
@@ -118,7 +118,29 @@ function Base.similar(
   return similar(promote_type(A, B), sz)
 end
 
-Base.collect(a::KroneckerArray) = kron(a.a, a.b)
+function flatten(t::Tuple{Tuple,Tuple,Vararg{Tuple}})
+  return (t[1]..., flatten(Base.tail(t))...)
+end
+function flatten(t::Tuple{Tuple})
+  return t[1]
+end
+flatten(::Tuple{}) = ()
+function interleave(x::Tuple, y::Tuple)
+  length(x) == length(y) || throw(ArgumentError("Tuples must have the same length."))
+  xy = ntuple(i -> (x[i], y[i]), length(x))
+  return flatten(xy)
+end
+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)))
+  c′ = permutedims(a′ .* b′, reverse(ntuple(identity, 2N)))
+  sz = ntuple(i -> size(a, i) * size(b, i), N)
+  return permutedims(reshape(c′, sz), reverse(ntuple(identity, N)))
+end
+kron_nd(a::AbstractMatrix, b::AbstractMatrix) = kron(a, b)
+kron_nd(a::AbstractVector, b::AbstractVector) = kron(a, b)
+
+Base.collect(a::KroneckerArray) = kron_nd(a.a, a.b)
 
 function Base.Array{T,N}(a::KroneckerArray{S,N}) where {T,S,N}
   return convert(Array{T,N}, collect(a))
@@ -150,10 +172,18 @@ function Base.show(io::IO, a::KroneckerArray)
   return nothing
 end
 
-⊗(a::AbstractVecOrMat, b::AbstractVecOrMat) = KroneckerArray(a, b)
+⊗(a::AbstractArray, b::AbstractArray) = KroneckerArray(a, b)
 ⊗(a::Number, b::Number) = a * b
-⊗(a::Number, b::AbstractVecOrMat) = a * b
-⊗(a::AbstractVecOrMat, b::Number) = a * b
+⊗(a::Number, b::AbstractArray) = a * b
+⊗(a::AbstractArray, b::Number) = a * b
+
+function Base.getindex(a::KroneckerArray, i::Integer)
+  return a[CartesianIndices(a)[i]]
+end
+
+function Base.getindex(a::KroneckerArray{<:Any,N}, I::Vararg{Integer,N}) where {N}
+  return error("Not implemented.")
+end
 
 function Base.getindex(a::KroneckerMatrix, i1::Integer, i2::Integer)
   GPUArraysCore.assertscalar("getindex")
@@ -162,9 +192,6 @@ function Base.getindex(a::KroneckerMatrix, i1::Integer, i2::Integer)
   k, l = size(a.b)
   return a.a[cld(i1, k), cld(i2, l)] * a.b[(i1 - 1) % k + 1, (i2 - 1) % l + 1]
 end
-function Base.getindex(a::KroneckerMatrix, i::Integer)
-  return a[CartesianIndices(a)[i]]
-end
 
 function Base.getindex(a::KroneckerVector, i::Integer)
   GPUArraysCore.assertscalar("getindex")
@@ -172,12 +199,14 @@ function Base.getindex(a::KroneckerVector, i::Integer)
   return a.a[cld(i, k)] * a.b[(i - 1) % k + 1]
 end
 
-function Base.getindex(a::KroneckerVector, i::CartesianProduct)
-  return a.a[i.a] ⊗ a.b[i.b]
-end
-function Base.getindex(a::KroneckerMatrix, i::CartesianProduct, j::CartesianProduct)
-  return a.a[i.a, j.a] ⊗ a.b[i.b, j.b]
+## function Base.getindex(a::KroneckerVector, i::CartesianProduct)
+##   return a.a[i.a] ⊗ a.b[i.b]
+## end
+function Base.getindex(a::KroneckerArray{<:Any,N}, I::Vararg{CartesianProduct,N}) where {N}
+  return a.a[map(Base.Fix2(getfield, :a), I)...] ⊗ a.b[map(Base.Fix2(getfield, :b), I)...]
 end
+# Fix ambigiuity error.
+Base.getindex(a::KroneckerArray{<:Any,0}) = a.a[] * a.b[]
 
 function Base.:(==)(a::KroneckerArray, b::KroneckerArray)
   return a.a == b.a && a.b == b.b
@@ -220,7 +249,7 @@ using LinearAlgebra:
   svd,
   svdvals,
   tr
-diagonal(a::AbstractVecOrMat) = Diagonal(a)
+diagonal(a::AbstractArray) = Diagonal(a)
 function diagonal(a::KroneckerArray)
   return Diagonal(a.a) ⊗ Diagonal(a.b)
 end
@@ -275,10 +304,10 @@ end
 function Base.:*(a::KroneckerQ, b::KroneckerQ)
   return (a.a * b.a) ⊗ (a.b * b.b)
 end
-function Base.:*(a::KroneckerQ, b::KroneckerMatrix)
+function Base.:*(a::KroneckerQ, b::KroneckerArray)
   return (a.a * b.a) ⊗ (a.b * b.b)
 end
-function Base.:*(a::KroneckerMatrix, b::KroneckerQ)
+function Base.:*(a::KroneckerArray, b::KroneckerQ)
   return (a.a * b.a) ⊗ (a.b * b.b)
 end
 function Base.adjoint(a::KroneckerQ)
diff --git a/test/test_basics.jl b/test/test_basics.jl
index 17892cc..1c10b53 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -1,4 +1,4 @@
-using KroneckerArrays: KroneckerArrays, ⊗, ×, diagonal
+using KroneckerArrays: KroneckerArrays, ⊗, ×, diagonal, kron_nd
 using LinearAlgebra: Diagonal, I, eigen, eigvals, lq, qr, svd, svdvals, tr
 using Test: @test, @testset
 
@@ -39,6 +39,16 @@ const elts = (Float32, Float64, ComplexF32, ComplexF64)
   end
   @test tr(a) ≈ tr(collect(a))
 
+  a = randn(elt, 2, 2, 2) ⊗ randn(elt, 3, 3, 3)
+  @test collect(a) ≈ kron_nd(a.a, a.b)
+  @test a[1 × 1, 1 × 1, 1 × 1] == a.a[1, 1, 1] * a.b[1, 1, 1]
+  @test a[1 × 3, 2 × 1, 2 × 2] == a.a[1, 2, 2] * a.b[3, 1, 2]
+  @test collect(a + a) ≈ 2 * collect(a)
+  @test collect(2a) ≈ 2 * collect(a)
+
+  a = randn(elt, 2, 2) ⊗ randn(elt, 3, 3)
+  b = randn(elt, 2, 2) ⊗ randn(elt, 3, 3)
+  c = a.a ⊗ b.b
   U, S, V = svd(a)
   @test collect(U * diagonal(S) * V') ≈ collect(a)
   @test svdvals(a) ≈ S
@@ -46,10 +56,12 @@ const elts = (Float32, Float64, ComplexF32, ComplexF64)
   @test collect(U'U) ≈ I
   @test collect(V * V') ≈ I
 
+  a = randn(elt, 2, 2) ⊗ randn(elt, 3, 3)
   D, V = eigen(a)
   @test collect(a * V) ≈ collect(V * diagonal(D))
   @test eigvals(a) ≈ D
 
+  a = randn(elt, 2, 2) ⊗ randn(elt, 3, 3)
   Q, R = qr(a)
   @test collect(Q * R) ≈ collect(a)
   @test collect(Q'Q) ≈ I