diff --git a/Project.toml b/Project.toml
index 29e0e8a..8da5421 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 = "0.1.5"
+version = "0.1.6"
 
 [deps]
 DerivableInterfaces = "6c5e35bf-e59e-4898-b73c-732dcc4ba65f"
diff --git a/src/KroneckerArrays.jl b/src/KroneckerArrays.jl
index 06fd869..3ae3fad 100644
--- a/src/KroneckerArrays.jl
+++ b/src/KroneckerArrays.jl
@@ -579,13 +579,17 @@ end
 using MatrixAlgebraKit:
   copy_input,
   eig_full,
+  eig_vals,
   eigh_full,
+  eigh_vals,
   qr_compact,
   qr_full,
+  left_null,
   left_orth,
   left_polar,
   lq_compact,
   lq_full,
+  right_null,
   right_orth,
   right_polar,
   svd_compact,
@@ -741,13 +745,17 @@ _copy_input_squareeye(f::F, a::SquareEye) where {F} = a
 
 for f in [
   :eig_full,
+  :eig_vals,
   :eigh_full,
+  :eigh_vals,
   :qr_compact,
   :qr_full,
+  :left_null,
   :left_orth,
   :left_polar,
   :lq_compact,
   :lq_full,
+  :right_null,
   :right_orth,
   :right_polar,
   :svd_compact,
@@ -791,6 +799,12 @@ end
 _initialize_output_squareeye(f::F, a) where {F} = initialize_output(f, a)
 _initialize_output_squareeye(f::F, a, alg) where {F} = initialize_output(f, a, alg)
 
+for f in [:left_null!, :right_null!]
+  @eval begin
+    _initialize_output_squareeye(::typeof($f), a::SquareEye) = a
+    _initialize_output_squareeye(::typeof($f), a::SquareEye, alg) = a
+  end
+end
 for f in [
   :eig_full!,
   :eigh_full!,
@@ -857,4 +871,74 @@ for f in [
   end
 end
 
+for f in [:left_null!, :right_null!]
+  f′ = Symbol("_", f, "_squareeye")
+  @eval begin
+    $f′(a, F; kwargs...) = $f(a, F; kwargs...)
+    $f′(a::SquareEye, F) = F
+  end
+  for T in [:SquareEyeKronecker, :KroneckerSquareEye]
+    @eval begin
+      function MatrixAlgebraKit.initialize_output(::typeof($f), a::$T)
+        return _initialize_output_squareeye($f, a.a) ⊗ _initialize_output_squareeye($f, a.b)
+      end
+      function MatrixAlgebraKit.$f(a::$T, F; kwargs1=(;), kwargs2=(;), kwargs...)
+        $f′(a.a, F.a; kwargs..., kwargs1...)
+        $f′(a.b, F.b; kwargs..., kwargs2...)
+        return F
+      end
+    end
+  end
+end
+
+function MatrixAlgebraKit.initialize_output(f::typeof(left_null!), a::SquareEyeSquareEye)
+  return _initialize_output_squareeye(f, a.a) ⊗ _initialize_output_squareeye(f, a.b)
+end
+function MatrixAlgebraKit.left_null!(
+  a::SquareEyeSquareEye, F; kwargs1=(;), kwargs2=(;), kwargs...
+)
+  return throw(MethodError(left_null!, (a, F)))
+end
+
+function MatrixAlgebraKit.initialize_output(f::typeof(right_null!), a::SquareEyeSquareEye)
+  return _initialize_output_squareeye(f, a.a) ⊗ _initialize_output_squareeye(f, a.b)
+end
+function MatrixAlgebraKit.right_null!(
+  a::SquareEyeSquareEye, F; kwargs1=(;), kwargs2=(;), kwargs...
+)
+  return throw(MethodError(right_null!, (a, F)))
+end
+
+for f in [:eig_vals!, :eigh_vals!, :svd_vals!]
+  @eval begin
+    _initialize_output_squareeye(::typeof($f), a::SquareEye) = parent(a)
+    _initialize_output_squareeye(::typeof($f), a::SquareEye, alg) = parent(a)
+  end
+end
+
+for f in [:eig_vals!, :eigh_vals!, :svd_vals!]
+  f′ = Symbol("_", f, "_squareeye")
+  @eval begin
+    $f′(a, F, alg; kwargs...) = $f(a, F, alg; kwargs...)
+    $f′(a, F, alg::SquareEyeAlgorithm) = F
+  end
+  for T in [:SquareEyeKronecker, :KroneckerSquareEye, :SquareEyeSquareEye]
+    @eval begin
+      function MatrixAlgebraKit.initialize_output(
+        ::typeof($f), a::$T, alg::KroneckerAlgorithm
+      )
+        return _initialize_output_squareeye($f, a.a, alg.a) ⊗
+               _initialize_output_squareeye($f, a.b, alg.b)
+      end
+      function MatrixAlgebraKit.$f(
+        a::$T, F, alg::KroneckerAlgorithm; kwargs1=(;), kwargs2=(;), kwargs...
+      )
+        $f′(a.a, F.a, alg.a; kwargs..., kwargs1...)
+        $f′(a.b, F.b, alg.b; kwargs..., kwargs2...)
+        return F
+      end
+    end
+  end
+end
+
 end
diff --git a/test/test_matrixalgebrakit.jl b/test/test_matrixalgebrakit.jl
index a26508d..82943cd 100644
--- a/test/test_matrixalgebrakit.jl
+++ b/test/test_matrixalgebrakit.jl
@@ -1,4 +1,4 @@
-using FillArrays: Eye
+using FillArrays: Eye, Ones
 using KroneckerArrays: ⊗, arguments
 using LinearAlgebra: Hermitian, I, diag, hermitianpart, norm
 using MatrixAlgebraKit:
@@ -124,13 +124,8 @@ end
 
   # TODO:
   # eig_trunc
-  # eig_vals
   # eigh_trunc
-  # eigh_vals
-  # left_null
-  # right_null
   # svd_trunc
-  # svd_vals
 
   for f in (eig_full, eigh_full)
     a = Eye(3) ⊗ parent(hermitianpart(randn(3, 3)))
@@ -154,17 +149,39 @@ end
     @test arguments(v, 2) isa Eye
   end
 
+  for f in (eig_vals, eigh_vals)
+    a = Eye(3) ⊗ parent(hermitianpart(randn(3, 3)))
+    d = @constinferred f(a)
+    d′ = f(Matrix(a))
+    @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs)
+    @test arguments(d, 1) isa Ones
+    @test arguments(d, 2) ≈ f(arguments(a, 2))
+
+    a = parent(hermitianpart(randn(3, 3))) ⊗ Eye(3)
+    d = @constinferred f(a)
+    d′ = f(Matrix(a))
+    @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs)
+    @test arguments(d, 2) isa Ones
+    @test arguments(d, 1) ≈ f(arguments(a, 1))
+
+    a = Eye(3) ⊗ Eye(3)
+    d = @constinferred f(a)
+    @test d == Ones(3) ⊗ Ones(3)
+    @test arguments(d, 1) isa Ones
+    @test arguments(d, 2) isa Ones
+  end
+
   for f in (
     left_orth, left_polar, lq_compact, lq_full, qr_compact, qr_full, right_orth, right_polar
   )
     a = Eye(3) ⊗ randn(3, 3)
-    x, y = f(a)
+    x, y = @constinferred f(a)
     @test x * y ≈ a
     @test arguments(x, 1) isa Eye
     @test arguments(y, 1) isa Eye
 
     a = randn(3, 3) ⊗ Eye(3)
-    x, y = f(a)
+    x, y = @constinferred f(a)
     @test x * y ≈ a
     @test arguments(x, 2) isa Eye
     @test arguments(y, 2) isa Eye
@@ -180,21 +197,21 @@ end
 
   for f in (svd_compact, svd_full)
     a = Eye(3) ⊗ randn(3, 3)
-    u, s, v = f(a)
+    u, s, v = @constinferred f(a)
     @test u * s * v ≈ a
     @test arguments(u, 1) isa Eye
     @test arguments(s, 1) isa Eye
     @test arguments(v, 1) isa Eye
 
     a = randn(3, 3) ⊗ Eye(3)
-    u, s, v = f(a)
+    u, s, v = @constinferred f(a)
     @test u * s * v ≈ a
     @test arguments(u, 2) isa Eye
     @test arguments(s, 2) isa Eye
     @test arguments(v, 2) isa Eye
 
     a = Eye(3) ⊗ Eye(3)
-    u, s, v = f(a)
+    u, s, v = @constinferred f(a)
     @test u * s * v ≈ a
     @test arguments(u, 1) isa Eye
     @test arguments(s, 1) isa Eye
@@ -203,4 +220,52 @@ end
     @test arguments(s, 2) isa Eye
     @test arguments(v, 2) isa Eye
   end
+
+  a = Eye(3) ⊗ randn(3, 3)
+  d = @constinferred svd_vals(a)
+  d′ = svd_vals(Matrix(a))
+  @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs)
+  @test arguments(d, 1) isa Ones
+  @test arguments(d, 2) ≈ svd_vals(arguments(a, 2))
+
+  a = randn(3, 3) ⊗ Eye(3)
+  d = @constinferred svd_vals(a)
+  d′ = svd_vals(Matrix(a))
+  @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs)
+  @test arguments(d, 2) isa Ones
+  @test arguments(d, 1) ≈ svd_vals(arguments(a, 1))
+
+  a = Eye(3) ⊗ Eye(3)
+  d = @constinferred svd_vals(a)
+  @test d == Ones(3) ⊗ Ones(3)
+  @test arguments(d, 1) isa Ones
+  @test arguments(d, 2) isa Ones
+
+  # left_null
+  a = Eye(3) ⊗ randn(3, 3)
+  n = @constinferred left_null(a)
+  @test norm(n' * a) ≈ 0
+  @test arguments(n, 1) isa Eye
+
+  a = randn(3, 3) ⊗ Eye(3)
+  n = @constinferred left_null(a)
+  @test norm(n' * a) ≈ 0
+  @test arguments(n, 2) isa Eye
+
+  a = Eye(3) ⊗ Eye(3)
+  @test_throws MethodError left_null(a)
+
+  # right_null
+  a = Eye(3) ⊗ randn(3, 3)
+  n = @constinferred right_null(a)
+  @test norm(a * n') ≈ 0
+  @test arguments(n, 1) isa Eye
+
+  a = randn(3, 3) ⊗ Eye(3)
+  n = @constinferred right_null(a)
+  @test norm(a * n') ≈ 0
+  @test arguments(n, 2) isa Eye
+
+  a = Eye(3) ⊗ Eye(3)
+  @test_throws MethodError right_null(a)
 end