diff --git a/Project.toml b/Project.toml
index bc1104b..1334477 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "ITensorBase"
 uuid = "4795dd04-0d67-49bb-8f44-b89c448a1dc7"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.2.2"
+version = "0.2.3"
 
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
@@ -10,6 +10,7 @@ FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MapBroadcast = "ebd9b9da-f48d-417c-9660-449667d60261"
 NamedDimsArrays = "60cbd0c0-df58-4cb7-918c-6f5607b73fde"
+TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 UnallocatedArrays = "43c9e47c-e622-40fb-bf18-a09fc8c466b6"
 UnspecifiedTypes = "42b3faec-625b-4613-8ddc-352bf9672b8d"
 VectorInterface = "409d34a3-91d5-4945-b6ec-7529ddf182d8"
@@ -34,6 +35,7 @@ LinearAlgebra = "1.10"
 MapBroadcast = "0.1.5"
 NamedDimsArrays = "0.7"
 SparseArraysBase = "0.5"
+TensorAlgebra = "0.3"
 UnallocatedArrays = "0.1.1"
 UnspecifiedTypes = "0.1.1"
 VectorInterface = "0.5"
diff --git a/src/quirks.jl b/src/quirks.jl
index c69606f..7b0d44f 100644
--- a/src/quirks.jl
+++ b/src/quirks.jl
@@ -20,46 +20,37 @@ hasqns(a::AbstractITensor) = all(hasqns, inds(a))
 # TODO: Investigate this and see if we can get rid of it.
 Base.Broadcast.extrude(a::AbstractITensor) = a
 
-# TODO: This is just a stand-in for truncated SVD
-# that only makes use of `maxdim`, just to get some
-# functionality running in `ITensorMPS.jl`.
-# Define a proper truncated SVD in
-# `MatrixAlgebra.jl`/`TensorAlgebra.jl`.
-function svd_truncated(a::AbstractITensor, codomain_inds; maxdim)
-  U, S, V = svd(a, codomain_inds)
-  r = Base.OneTo(min(maxdim, minimum(Int.(size(S)))))
-  u = commonind(U, S)
-  v = commonind(V, S)
-  us = uniqueinds(U, S)
-  vs = uniqueinds(V, S)
-  U′ = U[(us .=> :)..., u => r]
-  S′ = S[u => r, v => r]
-  V′ = V[v => r, (vs .=> :)...]
-  return U′, S′, V′
-end
+# See: https://github.com/JuliaLang/julia/blob/v1.11.4/base/namedtuple.jl#L269
+# `filter(f, ::NamedTuple)` is available in Julia v1.11, delete once
+# we drop support for Julia v1.10.
+filter_namedtuple(f, xs::NamedTuple) = xs[filter(k -> f(xs[k]), keys(xs))]
 
-using LinearAlgebra: qr, svd
-# TODO: Define this in `MatrixAlgebra.jl`/`TensorAlgebra.jl`.
-function factorize(
-  a::AbstractITensor, codomain_inds; maxdim=nothing, cutoff=nothing, ortho="left", kwargs...
+function translate_factorize_kwargs(;
+  # MatrixAlgebraKit.jl/TensorAlgebra.jl kwargs.
+  orth=nothing,
+  rtol=nothing,
+  maxrank=nothing,
+  # ITensors.jl kwargs.
+  ortho=nothing,
+  cutoff=nothing,
+  maxdim=nothing,
+  kwargs...,
 )
-  # TODO: Perform this intersection in `TensorAlgebra.qr`/`TensorAlgebra.svd`?
-  # See https://github.com/ITensor/NamedDimsArrays.jl/issues/22.
-  codomain_inds′ = if ortho == "left"
-    intersect(inds(a), codomain_inds)
-  elseif ortho == "right"
-    setdiff(inds(a), codomain_inds)
-  else
-    error("Bad `ortho` input.")
-  end
-  F1, F2 = if isnothing(maxdim) && isnothing(cutoff)
-    qr(a, codomain_inds′)
-  else
-    U, S, V = svd_truncated(a, codomain_inds′; maxdim)
-    U, S * V
-  end
-  if ortho == "right"
-    F2, F1 = F1, F2
-  end
-  return F1, F2, (; truncerr=zero(Bool),)
+  orth::Symbol = @something orth ortho :left
+  rtol = @something rtol cutoff Some(nothing)
+  maxrank = @something maxrank maxdim Some(nothing)
+  !isnothing(maxrank) && error("`maxrank` not supported yet.")
+  return filter_namedtuple(!isnothing, (; orth, rtol, maxrank, kwargs...))
+end
+
+using TensorAlgebra: TensorAlgebra, factorize
+function TensorAlgebra.factorize(a::AbstractITensor, codomain_inds, domain_inds; kwargs...)
+  return invoke(
+    factorize,
+    Tuple{AbstractNamedDimsArray,Any,Any},
+    a,
+    codomain_inds,
+    domain_inds;
+    translate_factorize_kwargs(; kwargs...)...,
+  )
 end
diff --git a/test/Project.toml b/test/Project.toml
index 2a687d6..99007e3 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -11,6 +11,7 @@ SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SparseArraysBase = "0d5efcca-f356-4864-8770-e1ed8d78f208"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 SymmetrySectors = "f8a8ad64-adbc-4fce-92f7-ffe2bb36a86e"
+TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
@@ -25,4 +26,5 @@ SafeTestsets = "0.1"
 SparseArraysBase = "0.5"
 Suppressor = "0.2"
 SymmetrySectors = "0.1"
+TensorAlgebra = "0.3"
 Test = "1.10"
diff --git a/test/test_basics.jl b/test/test_basics.jl
index 059d1e6..e69b5bd 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -19,8 +19,10 @@ using ITensorBase:
 using NamedDimsArrays: dename, name, named
 using SparseArraysBase: oneelement
 using SymmetrySectors: U1
+using LinearAlgebra: factorize
 using Test: @test, @test_broken, @test_throws, @testset
 
+const elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
 @testset "ITensorBase" begin
   @testset "Basics" begin
     elt = Float64
@@ -164,4 +166,29 @@ using Test: @test, @test_broken, @test_throws, @testset
     @test hasqns(j)
     @test hasqns(a)
   end
+  @testset "factorize" for elt in elts
+    i = Index(2)
+    j = Index(2)
+    a = randn(elt, i, j)
+    x, y = factorize(a, (i,))
+    @test a ≈ x * y
+    @test x isa ITensor
+    @test y isa ITensor
+    @test i ∈ inds(x)
+    @test j ∈ inds(y)
+    @test eltype(x) === elt
+    @test eltype(y) === elt
+    @test Int.(Tuple(size(x))) == (2, 2)
+    @test Int.(Tuple(size(y))) == (2, 2)
+
+    i = Index(2)
+    j = Index(2)
+    a = randn(elt, i) * randn(elt, j)
+    for kwargs in ((; rtol=1e-2), (; cutoff=1e-2))
+      x, y = factorize(a, (i,); kwargs...)
+      @test a ≈ x * y
+      @test Int.(Tuple(size(x))) == (2, 1)
+      @test Int.(Tuple(size(y))) == (1, 2)
+    end
+  end
 end