diff --git a/NDTensors/Project.toml b/NDTensors/Project.toml
index 5910135fb0..b4edf4d5de 100644
--- a/NDTensors/Project.toml
+++ b/NDTensors/Project.toml
@@ -1,7 +1,7 @@
 name = "NDTensors"
 uuid = "23ae76d9-e61a-49c4-8f12-3f1a16adf9cf"
 authors = ["Matthew Fishman <mfishman@flatironinstitute.org>"]
-version = "0.3.61"
+version = "0.3.62"
 
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
diff --git a/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/arraylayouts.jl b/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/arraylayouts.jl
index 7486d443c7..069d367cf6 100644
--- a/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/arraylayouts.jl
+++ b/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/arraylayouts.jl
@@ -1,7 +1,7 @@
-using ArrayLayouts: ArrayLayouts, MemoryLayout, MulAdd
+using ArrayLayouts: ArrayLayouts, DualLayout, MemoryLayout, MulAdd
 using BlockArrays: BlockLayout
 using ..SparseArrayInterface: SparseLayout
-using ..TypeParameterAccessors: similartype
+using ..TypeParameterAccessors: parenttype, similartype
 
 function ArrayLayouts.MemoryLayout(arraytype::Type{<:BlockSparseArrayLike})
   outer_layout = typeof(MemoryLayout(blockstype(arraytype)))
@@ -9,6 +9,19 @@ function ArrayLayouts.MemoryLayout(arraytype::Type{<:BlockSparseArrayLike})
   return BlockLayout{outer_layout,inner_layout}()
 end
 
+# TODO: Generalize to `BlockSparseVectorLike`/`AnyBlockSparseVector`.
+function ArrayLayouts.MemoryLayout(
+  arraytype::Type{<:Adjoint{<:Any,<:AbstractBlockSparseVector}}
+)
+  return DualLayout{typeof(MemoryLayout(parenttype(arraytype)))}()
+end
+# TODO: Generalize to `BlockSparseVectorLike`/`AnyBlockSparseVector`.
+function ArrayLayouts.MemoryLayout(
+  arraytype::Type{<:Transpose{<:Any,<:AbstractBlockSparseVector}}
+)
+  return DualLayout{typeof(MemoryLayout(parenttype(arraytype)))}()
+end
+
 function Base.similar(
   mul::MulAdd{<:BlockLayout{<:SparseLayout},<:BlockLayout{<:SparseLayout},<:Any,<:Any,A,B},
   elt::Type,
diff --git a/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl b/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl
index dfb797caaa..e8d1e5e15b 100644
--- a/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl
+++ b/NDTensors/src/lib/BlockSparseArrays/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl
@@ -158,6 +158,13 @@ function Base.similar(
   return similar(arraytype, eltype(arraytype), axes)
 end
 
+# Fixes ambiguity error.
+function Base.similar(
+  arraytype::Type{<:BlockSparseArrayLike}, axes::Tuple{Base.OneTo,Vararg{Base.OneTo}}
+)
+  return similar(arraytype, eltype(arraytype), axes)
+end
+
 # Needed by `BlockArrays` matrix multiplication interface
 # TODO: This fixes an ambiguity error with `OffsetArrays.jl`, but
 # is only appears to be needed in older versions of Julia like v1.6.
@@ -221,7 +228,7 @@ function Base.similar(
 end
 
 # Fixes ambiguity error.
-function Base.similar(a::BlockSparseArrayLike{<:Any,0}, elt::Type, axes::Tuple{})
+function Base.similar(a::BlockSparseArrayLike, elt::Type, axes::Tuple{})
   return blocksparse_similar(a, elt, axes)
 end
 
diff --git a/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/arraylayouts.jl b/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/arraylayouts.jl
index 7543ad434d..483c53f835 100644
--- a/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/arraylayouts.jl
+++ b/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/arraylayouts.jl
@@ -1,15 +1,21 @@
-using ArrayLayouts: ArrayLayouts, MatMulMatAdd
+using ArrayLayouts: ArrayLayouts, Dot, MatMulMatAdd, MatMulVecAdd, MulAdd
 using BlockArrays: BlockLayout
 using ..SparseArrayInterface: SparseLayout
-using LinearAlgebra: mul!
+using LinearAlgebra: dot, mul!
 
 function blocksparse_muladd!(
-  α::Number, a1::AbstractMatrix, a2::AbstractMatrix, β::Number, a_dest::AbstractMatrix
+  α::Number, a1::AbstractArray, a2::AbstractArray, β::Number, a_dest::AbstractArray
 )
   mul!(blocks(a_dest), blocks(a1), blocks(a2), α, β)
   return a_dest
 end
 
+function blocksparse_matmul!(m::MulAdd)
+  α, a1, a2, β, a_dest = m.α, m.A, m.B, m.β, m.C
+  blocksparse_muladd!(α, a1, a2, β, a_dest)
+  return a_dest
+end
+
 function ArrayLayouts.materialize!(
   m::MatMulMatAdd{
     <:BlockLayout{<:SparseLayout},
@@ -17,7 +23,26 @@ function ArrayLayouts.materialize!(
     <:BlockLayout{<:SparseLayout},
   },
 )
-  α, a1, a2, β, a_dest = m.α, m.A, m.B, m.β, m.C
-  blocksparse_muladd!(α, a1, a2, β, a_dest)
-  return a_dest
+  blocksparse_matmul!(m)
+  return m.C
+end
+function ArrayLayouts.materialize!(
+  m::MatMulVecAdd{
+    <:BlockLayout{<:SparseLayout},
+    <:BlockLayout{<:SparseLayout},
+    <:BlockLayout{<:SparseLayout},
+  },
+)
+  blocksparse_matmul!(m)
+  return m.C
+end
+
+function blocksparse_dot(a1::AbstractArray, a2::AbstractArray)
+  # TODO: Add a check that the blocking of `a1` and `a2` are
+  # the same, or the same up to a reshape.
+  return dot(blocks(a1), blocks(a2))
+end
+
+function Base.copy(d::Dot{<:BlockLayout{<:SparseLayout},<:BlockLayout{<:SparseLayout}})
+  return blocksparse_dot(d.A, d.B)
 end
diff --git a/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/blocksparsearrayinterface.jl b/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/blocksparsearrayinterface.jl
index fbb5f220f4..601ead6c53 100644
--- a/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/blocksparsearrayinterface.jl
+++ b/NDTensors/src/lib/BlockSparseArrays/src/blocksparsearrayinterface/blocksparsearrayinterface.jl
@@ -184,7 +184,7 @@ reverse_index(index::CartesianIndex) = CartesianIndex(reverse(Tuple(index)))
 
 # Represents the array of arrays of a `Transpose`
 # wrapping a block spare array, i.e. `blocks(array)` where `a` is a `Transpose`.
-struct SparseTransposeBlocks{T,BlockType<:AbstractMatrix{T},Array<:Transpose{T}} <:
+struct SparseTransposeBlocks{T,BlockType<:AbstractArray{T},Array<:Transpose{T}} <:
        AbstractSparseMatrix{BlockType}
   array::Array
 end
@@ -219,7 +219,7 @@ end
 
 # Represents the array of arrays of a `Adjoint`
 # wrapping a block spare array, i.e. `blocks(array)` where `a` is a `Adjoint`.
-struct SparseAdjointBlocks{T,BlockType<:AbstractMatrix{T},Array<:Adjoint{T}} <:
+struct SparseAdjointBlocks{T,BlockType<:AbstractArray{T},Array<:Adjoint{T}} <:
        AbstractSparseMatrix{BlockType}
   array::Array
 end
diff --git a/NDTensors/src/lib/BlockSparseArrays/test/test_basics.jl b/NDTensors/src/lib/BlockSparseArrays/test/test_basics.jl
index 27012d32c9..4374be541c 100644
--- a/NDTensors/src/lib/BlockSparseArrays/test/test_basics.jl
+++ b/NDTensors/src/lib/BlockSparseArrays/test/test_basics.jl
@@ -16,7 +16,7 @@ using BlockArrays:
   mortar
 using Compat: @compat
 using GPUArraysCore: @allowscalar
-using LinearAlgebra: Adjoint, mul!, norm
+using LinearAlgebra: Adjoint, dot, mul!, norm
 using NDTensors.BlockSparseArrays:
   @view!,
   BlockSparseArray,
@@ -575,7 +575,11 @@ using .NDTensorsTestUtils: devices_list, is_supported_eltype
       a[b] = randn(elt, size(a[b]))
     end
     @test isassigned(a, 1, 1)
+    @test isassigned(a, 1, 1, 1)
+    @test !isassigned(a, 1, 1, 2)
     @test isassigned(a, 5, 7)
+    @test isassigned(a, 5, 7, 1)
+    @test !isassigned(a, 5, 7, 2)
     @test !isassigned(a, 0, 1)
     @test !isassigned(a, 5, 8)
     @test isassigned(a, Block(1), Block(1))
@@ -852,6 +856,16 @@ using .NDTensorsTestUtils: devices_list, is_supported_eltype
       @allowscalar @test Array(a_dest) ≈ Array(a1′) * Array(a2′)
     end
   end
+  @testset "Dot product" begin
+    a1 = dev(BlockSparseArray{elt}([2, 3, 4]))
+    a1[Block(1)] = dev(randn(elt, size(@view(a1[Block(1)]))))
+    a1[Block(3)] = dev(randn(elt, size(@view(a1[Block(3)]))))
+    a2 = dev(BlockSparseArray{elt}([2, 3, 4]))
+    a2[Block(2)] = dev(randn(elt, size(@view(a1[Block(2)]))))
+    a2[Block(3)] = dev(randn(elt, size(@view(a1[Block(3)]))))
+    @test a1' * a2 ≈ Array(a1)' * Array(a2)
+    @test dot(a1, a2) ≈ a1' * a2
+  end
   @testset "TensorAlgebra" begin
     a1 = dev(BlockSparseArray{elt}([2, 3], [2, 3]))
     a1[Block(1, 1)] = dev(randn(elt, size(@view(a1[Block(1, 1)]))))
diff --git a/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/arraylayouts.jl b/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/arraylayouts.jl
index 038689be8a..58176846ca 100644
--- a/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/arraylayouts.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/arraylayouts.jl
@@ -1,13 +1,41 @@
-using ArrayLayouts: ArrayLayouts, MatMulMatAdd
+using ArrayLayouts: ArrayLayouts, Dot, DualLayout, MatMulMatAdd, MatMulVecAdd, MulAdd
+using LinearAlgebra: Adjoint, Transpose
+using ..TypeParameterAccessors: parenttype
 
 function ArrayLayouts.MemoryLayout(arraytype::Type{<:SparseArrayLike})
   return SparseLayout()
 end
 
-function ArrayLayouts.materialize!(
-  m::MatMulMatAdd{<:AbstractSparseLayout,<:AbstractSparseLayout,<:AbstractSparseLayout}
+# TODO: Generalize to `SparseVectorLike`/`AnySparseVector`.
+function ArrayLayouts.MemoryLayout(arraytype::Type{<:Adjoint{<:Any,<:AbstractSparseVector}})
+  return DualLayout{typeof(MemoryLayout(parenttype(arraytype)))}()
+end
+# TODO: Generalize to `SparseVectorLike`/`AnySparseVector`.
+function ArrayLayouts.MemoryLayout(
+  arraytype::Type{<:Transpose{<:Any,<:AbstractSparseVector}}
 )
+  return DualLayout{typeof(MemoryLayout(parenttype(arraytype)))}()
+end
+
+function sparse_matmul!(m::MulAdd)
   α, a1, a2, β, a_dest = m.α, m.A, m.B, m.β, m.C
   sparse_mul!(a_dest, a1, a2, α, β)
   return a_dest
 end
+
+function ArrayLayouts.materialize!(
+  m::MatMulMatAdd{<:AbstractSparseLayout,<:AbstractSparseLayout,<:AbstractSparseLayout}
+)
+  sparse_matmul!(m)
+  return m.C
+end
+function ArrayLayouts.materialize!(
+  m::MatMulVecAdd{<:AbstractSparseLayout,<:AbstractSparseLayout,<:AbstractSparseLayout}
+)
+  sparse_matmul!(m)
+  return m.C
+end
+
+function Base.copy(d::Dot{<:SparseLayout,<:SparseLayout})
+  return sparse_dot(d.A, d.B)
+end
diff --git a/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/SparseArrayInterfaceLinearAlgebraExt.jl b/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/SparseArrayInterfaceLinearAlgebraExt.jl
index 7a444297f7..633506d630 100644
--- a/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/SparseArrayInterfaceLinearAlgebraExt.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/SparseArrayInterfaceLinearAlgebraExt.jl
@@ -1,4 +1,4 @@
-using LinearAlgebra: mul!, norm
+using LinearAlgebra: dot, mul!, norm
 
 sparse_norm(a::AbstractArray, p::Real=2) = norm(sparse_storage(a))
 
@@ -9,6 +9,14 @@ function mul_indices(I1::CartesianIndex{2}, I2::CartesianIndex{2})
   return CartesianIndex(I1[1], I2[2])
 end
 
+# TODO: Is this needed? Maybe when multiplying vectors?
+function mul_indices(I1::CartesianIndex{1}, I2::CartesianIndex{1})
+  if I1 ≠ I2
+    return nothing
+  end
+  return CartesianIndex(I1)
+end
+
 function default_mul!!(
   a_dest::AbstractMatrix,
   a1::AbstractMatrix,
@@ -28,9 +36,9 @@ end
 
 # a1 * a2 * α + a_dest * β
 function sparse_mul!(
-  a_dest::AbstractMatrix,
-  a1::AbstractMatrix,
-  a2::AbstractMatrix,
+  a_dest::AbstractArray,
+  a1::AbstractArray,
+  a2::AbstractArray,
   α::Number=true,
   β::Number=false;
   (mul!!)=(default_mul!!),
@@ -45,3 +53,26 @@ function sparse_mul!(
   end
   return a_dest
 end
+
+function sparse_dot(a1::AbstractArray, a2::AbstractArray)
+  # This requires that `a1` and `a2` have the same shape.
+  # TODO: Generalize (Base supports dot products of
+  # arrays with the same length but different sizes).
+  size(a1) == size(a2) ||
+    throw(DimensionMismatch("Sizes $(size(a1)) and $(size(a2)) don't match."))
+  dot_dest = zero(Base.promote_op(dot, eltype(a1), eltype(a2)))
+  # TODO: First check if the number of stored elements (`nstored`, to be renamed
+  # `stored_length`) is smaller in `a1` or `a2` and use whicheven one is smallar
+  # as the outer loop.
+  for I1 in stored_indices(a1)
+    # TODO: Overload and use `Base.isstored(a, I) = I in stored_indices(a)` instead.
+    # TODO: This assumes fast lookup of indices, which may not always be the case.
+    # It could be better to loop over `stored_indices(a2)` and check that
+    # `I1 == I2` instead (say using `mul_indices(I1, I2)`. We could have a trait
+    # `HasFastIsStored(a::AbstractArray)` to choose between the two.
+    if I1 in stored_indices(a2)
+      dot_dest += dot(a1[I1], a2[I1])
+    end
+  end
+  return dot_dest
+end
diff --git a/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/indexing.jl b/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/indexing.jl
index 216c03e7ac..ae0f6f6d61 100644
--- a/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/indexing.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/indexing.jl
@@ -166,7 +166,10 @@ end
 function sparse_isassigned(a::AbstractArray{<:Any,N}, I::CartesianIndex{N}) where {N}
   return sparse_isassigned(a, Tuple(I)...)
 end
-function sparse_isassigned(a::AbstractArray{<:Any,N}, I::Vararg{Integer,N}) where {N}
+function sparse_isassigned(a::AbstractArray, I::Integer...)
+  # Check trailing dimensions are one. This is needed in generic
+  # AbstractArray show when `a isa AbstractVector`.
+  all(d -> isone(I[d]), (ndims(a) + 1):length(I)) || return false
   return all(dim -> I[dim] ∈ axes(a, dim), 1:ndims(a))
 end
 
diff --git a/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl b/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl
index 05b2cb3072..e1ca4f0661 100644
--- a/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl
@@ -32,6 +32,10 @@ function LinearAlgebra.mul!(
   return a_dest
 end
 
+function LinearAlgebra.dot(a1::SparseArray, a2::SparseArray)
+  return SparseArrayInterface.sparse_dot(a1, a2)
+end
+
 # AbstractArray interface
 Base.size(a::SparseArray) = a.dims
 function Base.similar(a::SparseArray, elt::Type, dims::Tuple{Vararg{Int}})
diff --git a/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl b/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl
index cd233f4ff1..743f457d43 100644
--- a/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl
@@ -1,5 +1,5 @@
 @eval module $(gensym())
-using LinearAlgebra: mul!, norm
+using LinearAlgebra: dot, mul!, norm
 using NDTensors.SparseArrayInterface: SparseArrayInterface
 include("SparseArrayInterfaceTestUtils/SparseArrayInterfaceTestUtils.jl")
 using .SparseArrayInterfaceTestUtils.AbstractSparseArrays: AbstractSparseArrays
@@ -299,6 +299,18 @@ using Test: @test, @testset
   @test a_dest isa SparseArray{elt}
   @test SparseArrayInterface.nstored(a_dest) == 2
 
+  # Dot product
+  a1 = SparseArray{elt}(4)
+  a1[1] = randn()
+  a1[3] = randn()
+  a2 = SparseArray{elt}(4)
+  a2[2] = randn()
+  a2[3] = randn()
+  a_dest = a1' * a2
+  @test a_dest isa elt
+  @test a_dest ≈ Array(a1)' * Array(a2)
+  @test a_dest ≈ dot(a1, a2)
+
   # In-place matrix multiplication
   a1 = SparseArray{elt}(2, 3)
   a1[1, 2] = 12
diff --git a/NDTensors/src/lib/TensorAlgebra/src/LinearAlgebraExtensions/qr.jl b/NDTensors/src/lib/TensorAlgebra/src/LinearAlgebraExtensions/qr.jl
index 7230258e7c..7c0d3f0ebb 100644
--- a/NDTensors/src/lib/TensorAlgebra/src/LinearAlgebraExtensions/qr.jl
+++ b/NDTensors/src/lib/TensorAlgebra/src/LinearAlgebraExtensions/qr.jl
@@ -1,3 +1,4 @@
+using ArrayLayouts: LayoutMatrix
 using LinearAlgebra: LinearAlgebra, qr
 using ..TensorAlgebra:
   TensorAlgebra,
@@ -8,6 +9,8 @@ using ..TensorAlgebra:
   fusedims,
   splitdims
 
+# TODO: Define as `tensor_qr`.
+# TODO: This look generic but doesn't work for `BlockSparseArrays`.
 function _qr(a::AbstractArray, biperm::BlockedPermutation{2})
   a_matricized = fusedims(a, biperm)
 
@@ -38,6 +41,12 @@ function LinearAlgebra.qr(a::AbstractMatrix, biperm::BlockedPermutation{2})
   return _qr(a, biperm)
 end
 
+# Fix ambiguity error with `ArrayLayouts`.
+function LinearAlgebra.qr(a::LayoutMatrix, biperm::BlockedPermutation{2})
+  return _qr(a, biperm)
+end
+
+# TODO: Define in terms of an inner function `_qr` or `tensor_qr`.
 function LinearAlgebra.qr(
   a::AbstractArray, labels_a::Tuple, labels_q::Tuple, labels_r::Tuple
 )
@@ -50,3 +59,10 @@ function LinearAlgebra.qr(
 )
   return qr(a, blockedperm_indexin(labels_a, labels_q, labels_r))
 end
+
+# Fix ambiguity error with `ArrayLayouts`.
+function LinearAlgebra.qr(
+  a::LayoutMatrix, labels_a::Tuple, labels_q::Tuple, labels_r::Tuple
+)
+  return qr(a, blockedperm_indexin(labels_a, labels_q, labels_r))
+end