diff --git a/Project.toml b/Project.toml
index 72d74f5..720a92b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "BlockSparseArrays"
 uuid = "2c9a651f-6452-4ace-a6ac-809f4280fbb4"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.7.12"
+version = "0.7.13"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/BlockSparseArrays.jl b/src/BlockSparseArrays.jl
index ec996e0..4229343 100644
--- a/src/BlockSparseArrays.jl
+++ b/src/BlockSparseArrays.jl
@@ -45,6 +45,7 @@ include("blocksparsearray/blockdiagonalarray.jl")
 include("BlockArraysSparseArraysBaseExt/BlockArraysSparseArraysBaseExt.jl")
 
 # factorizations
+include("factorizations/tensorproducts.jl")
 include("factorizations/svd.jl")
 include("factorizations/truncation.jl")
 include("factorizations/qr.jl")
diff --git a/src/blocksparsearrayinterface/getunstoredblock.jl b/src/blocksparsearrayinterface/getunstoredblock.jl
index 36cadde..d221286 100644
--- a/src/blocksparsearrayinterface/getunstoredblock.jl
+++ b/src/blocksparsearrayinterface/getunstoredblock.jl
@@ -6,16 +6,17 @@ struct GetUnstoredBlock{Axes}
 end
 
 @inline function (f::GetUnstoredBlock)(
-  a::AbstractArray{<:Any,N}, I::Vararg{Int,N}
-) where {N}
-  # TODO: Make sure this works for sparse or block sparse blocks, immutable
-  # blocks, diagonal blocks, etc.!
-  b_ax = ntuple(ndims(a)) do d
+  ::Type{<:AbstractArray{A,N}}, I::Vararg{Int,N}
+) where {A,N}
+  ax = ntuple(N) do d
     return only(axes(f.axes[d][Block(I[d])]))
   end
-  b = similar(eltype(a), b_ax)
-  zero!(b)
-  return b
+  return zero!(similar(A, ax))
+end
+@inline function (f::GetUnstoredBlock)(
+  a::AbstractArray{<:Any,N}, I::Vararg{Int,N}
+) where {N}
+  return f(typeof(a), I...)
 end
 # TODO: Use `Base.to_indices`.
 @inline function (f::GetUnstoredBlock)(
@@ -25,16 +26,17 @@ end
 end
 
 # TODO: this is a hack and is also type-unstable
+using LinearAlgebra: Diagonal
+using TypeParameterAccessors: similartype
 function (f::GetUnstoredBlock)(
-  a::AbstractMatrix{LinearAlgebra.Diagonal{T,V}}, I::Vararg{Int,2}
-) where {T,V}
-  b_size = ntuple(ndims(a)) do d
-    return length(f.axes[d][Block(I[d])])
+  ::Type{<:AbstractMatrix{<:Diagonal{<:Any,V}}}, I::Vararg{Int,2}
+) where {V}
+  ax = ntuple(2) do d
+    return only(axes(f.axes[d][Block(I[d])]))
   end
-  if I[1] == I[2]
-    diag = zero!(similar(V, b_size[1]))
-    return LinearAlgebra.Diagonal{T,V}(diag)
+  if allequal(I)
+    return Diagonal(zero!(similar(V, first(ax))))
   else
-    return zeros(T, b_size...)
+    return zero!(similar(similartype(V, typeof(ax)), ax))
   end
 end
diff --git a/src/factorizations/svd.jl b/src/factorizations/svd.jl
index be7ca75..b57b8eb 100644
--- a/src/factorizations/svd.jl
+++ b/src/factorizations/svd.jl
@@ -25,10 +25,11 @@ end
 function similar_output(
   ::typeof(svd_compact!), A, S_axes, alg::MatrixAlgebraKit.AbstractAlgorithm
 )
-  U = similar(A, axes(A, 1), S_axes[1])
-  S = similar(A, BlockType(diagonaltype(realtype(blocktype(A)))), S_axes)
-  Vt = similar(A, S_axes[2], axes(A, 2))
-  return U, S, Vt
+  BU, BS, BVᴴ = fieldtypes(Base.promote_op(svd_compact!, blocktype(A), typeof(alg.alg)))
+  U = similar(A, BlockType(BU), (axes(A, 1), S_axes[1]))
+  S = similar(A, BlockType(BS), S_axes)
+  Vᴴ = similar(A, BlockType(BVᴴ), (S_axes[2], axes(A, 2)))
+  return U, S, Vᴴ
 end
 
 function MatrixAlgebraKit.initialize_output(
@@ -48,9 +49,8 @@ function MatrixAlgebraKit.initialize_output(
   bcolIs = Int.(last.(Tuple.(bIs)))
   for bI in eachblockstoredindex(A)
     row, col = Int.(Tuple(bI))
-    len = minimum(length, (brows[row], bcols[col]))
-    u_axes[col] = brows[row][Base.OneTo(len)]
-    v_axes[col] = bcols[col][Base.OneTo(len)]
+    u_axes[col] = infimum(brows[row], bcols[col])
+    v_axes[col] = infimum(bcols[col], brows[row])
   end
 
   # fill in values for blocks that aren't present, pairing them in order of occurence
@@ -58,9 +58,8 @@ function MatrixAlgebraKit.initialize_output(
   emptyrows = setdiff(1:bm, browIs)
   emptycols = setdiff(1:bn, bcolIs)
   for (row, col) in zip(emptyrows, emptycols)
-    len = minimum(length, (brows[row], bcols[col]))
-    u_axes[col] = brows[row][Base.OneTo(len)]
-    v_axes[col] = bcols[col][Base.OneTo(len)]
+    u_axes[col] = infimum(brows[row], bcols[col])
+    v_axes[col] = infimum(bcols[col], brows[row])
   end
 
   u_axis = mortar_axis(u_axes)
diff --git a/src/factorizations/tensorproducts.jl b/src/factorizations/tensorproducts.jl
new file mode 100644
index 0000000..bbf02ae
--- /dev/null
+++ b/src/factorizations/tensorproducts.jl
@@ -0,0 +1,19 @@
+function infimum(r1::AbstractUnitRange, r2::AbstractUnitRange)
+  (isone(first(r1)) && isone(first(r2))) ||
+    throw(ArgumentError("infimum only defined for ranges starting at 1"))
+  if length(r1) ≤ length(r2)
+    return r1
+  else
+    return r1[r2]
+  end
+end
+
+function supremum(r1::AbstractUnitRange, r2::AbstractUnitRange)
+  (isone(first(r1)) && isone(first(r2))) ||
+    throw(ArgumentError("supremum only defined for ranges starting at 1"))
+  if length(r1) ≥ length(r2)
+    return r1
+  else
+    return r2
+  end
+end