diff --git a/src/fast_linalg.jl b/src/fast_linalg.jl
index 82561d999..168d2afec 100644
--- a/src/fast_linalg.jl
+++ b/src/fast_linalg.jl
@@ -97,19 +97,19 @@ function fast_X_A_Xt!(out::PSDMatrix, A::PSDMatrix, X::AbstractMatrix)
     return out
 end
 
-"""
-    alloc_free_get_U!(C::Cholesky)
-
-Allocation-free version of `C.U`.
-
-THIS MODIFIES `C.factors` SO AFTERWARDS `C` SHOULD NOT BE USED ANYMORE!
-"""
-function alloc_free_get_U!(C::Cholesky)
-    Cuplo = getfield(C, :uplo)
-    Cfactors = getfield(C, :factors)
-    if Cuplo === LinearAlgebra.char_uplo(:U)
-        return getupperright!(Cfactors)
-    else
-        return getupperright!(Cfactors')
-    end
-end
+# """
+#     alloc_free_get_U!(C::Cholesky)
+
+# Allocation-free version of `C.U`.
+
+# THIS MODIFIES `C.factors` SO AFTERWARDS `C` SHOULD NOT BE USED ANYMORE!
+# """
+# function alloc_free_get_U!(C::Cholesky)
+#     Cuplo = getfield(C, :uplo)
+#     Cfactors = getfield(C, :factors)
+#     if Cuplo === LinearAlgebra.char_uplo(:U)
+#         return getupperright!(Cfactors)
+#     else
+#         return getupperright!(Cfactors')
+#     end
+# end
diff --git a/src/kronecker.jl b/src/kronecker.jl
index 57f8645f4..3c99346db 100644
--- a/src/kronecker.jl
+++ b/src/kronecker.jl
@@ -27,13 +27,26 @@ IsometricKroneckerProduct(ldim::Integer, B::AbstractVector) =
     IsometricKroneckerProduct(ldim, reshape(B, :, 1))
 
 const IKP = IsometricKroneckerProduct
-get_right_factor(K::IKP) = K.B
-get_left_factor_dim(K::IKP) = K.B
 
 Kronecker.getmatrices(K::IKP) = (I(K.ldim), K.B)
 
 Base.zero(A::IKP) = IsometricKroneckerProduct(A.ldim, zero(A.B))
 Base.one(A::IKP) = IsometricKroneckerProduct(A.ldim, one(A.B))
+copy!(A::IKP, B::IKP) = begin
+    check_same_size(A, B)
+    copy!(A.B, B.B)
+    return A
+end
+copy(A::IKP) = IsometricKroneckerProduct(A.ldim, copy(A.B))
+similar(A::IKP) = IsometricKroneckerProduct(A.ldim, similar(A.B))
+Base.size(K::IKP) = (K.ldim * size(K.B, 1), K.ldim * size(K.B, 2))
+
+# conversion
+Base.convert(::Type{T}, K::IKP) where {T<:IKP} =
+    K isa T ? K : T(K)
+function IKP{T,TB}(K::IKP) where {T,TB}
+    IKP(K.ldim, convert(TB, K.B))
+end
 
 function Base.:*(A::IKP, B::IKP)
     @assert A.ldim == B.ldim
@@ -55,7 +68,7 @@ function check_matmul_sizes(A::IKP, B::IKP)
     # For A * B
     Ad, Bd = A.ldim, B.ldim
     An, Am, Bn, Bm = size(A)..., size(B)...
-    if !(A.ldim == B.ldim) || !(Am == Bnb)
+    if !(A.ldim == B.ldim) || !(Am == Bn)
         throw(
             DimensionMismatch(
                 "Matrix multiplication not compatible: A has size ($Ad⋅$An,$Ad⋅$Am), B has size ($Bd⋅$Bn,$Bd⋅$Bm)",
@@ -93,6 +106,18 @@ Base.:\(A::IKP, B::IKP) = begin
     return IsometricKroneckerProduct(A.ldim, A.B \ B.B)
 end
 
+mul!(A::IKP, B::IKP, C::IKP) = begin
+    check_matmul_sizes(A, B, C)
+    mul!(A.B, B.B, C.B)
+    return A
+end
+mul!(A::IKP, B::IKP, C::IKP, alpha::Number, beta::Number) = begin
+    check_matmul_sizes(A, B, C)
+    mul!(A.B, B.B, C.B, alpha, beta)
+    return A
+end
+
+# fast_linalg.jl
 _matmul!(A::IKP, B::IKP, C::IKP) = begin
     check_matmul_sizes(A, B, C)
     _matmul!(A.B, B.B, C.B)
@@ -105,7 +130,7 @@ _matmul!(A::IKP{T}, B::IKP{T}, C::IKP{T}) where {T<:LinearAlgebra.BlasFloat} = b
 end
 _matmul!(A::IKP, B::IKP, C::IKP, alpha::Number, beta::Number) = begin
     check_matmul_sizes(A, B, C)
-    _matmul!(A.B, B.B, C.B)
+    _matmul!(A.B, B.B, C.B, alpha, beta)
     return A
 end
 _matmul!(
@@ -119,21 +144,6 @@ _matmul!(
     _matmul!(A.B, B.B, C.B, alpha, beta)
     return A
 end
-copy!(A::IKP, B::IKP) = begin
-    check_same_size(A, B)
-    copy!(A.B, B.B)
-    return A
-end
-copy(A::IKP) = IsometricKroneckerProduct(A.ldim, copy(A.B))
-similar(A::IKP) = IsometricKroneckerProduct(A.ldim, similar(A.B))
-Base.size(K::IKP) = (K.ldim * size(K.B, 1), K.ldim * size(K.B, 2))
-
-# conversion
-Base.convert(::Type{T}, K::IKP) where {T<:IKP} =
-    K isa T ? K : T(K)
-function IKP{T,TB}(K::IKP) where {T,TB}
-    IKP(K.ldim, convert(TB, K.B))
-end
 
 """
 Allocation-free reshape
@@ -154,12 +164,7 @@ function mul_vectrick!(x::AbstractVecOrMat, A::IKP, v::AbstractVecOrMat)
     return x
 end
 function mul_vectrick!(
-    x::AbstractVecOrMat,
-    A::IKP,
-    v::AbstractVecOrMat,
-    alpha::Number,
-    beta::Number,
-)
+    x::AbstractVecOrMat, A::IKP, v::AbstractVecOrMat, alpha::Number, beta::Number)
     N = A.B
     c, d = size(N)
 
@@ -169,39 +174,46 @@ function mul_vectrick!(
     return x
 end
 
-_matmul!(C::AbstractVecOrMat, A::IKP, B::AbstractVecOrMat) = mul_vectrick!(C, A, B)
 mul!(C::AbstractMatrix, A::IKP, B::AbstractMatrix) = mul_vectrick!(C, A, B)
 mul!(C::AbstractMatrix, A::IKP, B::Adjoint{T,<:AbstractMatrix{T}}) where {T} =
     mul_vectrick!(C, A, B)
 mul!(C::AbstractVector, A::IKP, B::AbstractVector) = mul_vectrick!(C, A, B)
 
-_matmul!(
-    C::AbstractVecOrMat{T},
-    A::IKP{T},
-    B::AbstractVecOrMat{T},
-) where {T<:LinearAlgebra.BlasFloat} = mul_vectrick!(C, A, B)
-_matmul!(C::AbstractVecOrMat, A::AbstractVecOrMat, B::IKP) = _matmul!(C', B', A')
-_matmul!(
-    C::AbstractVecOrMat{T},
-    A::AbstractVecOrMat{T},
-    B::IKP{T},
-) where {T<:LinearAlgebra.BlasFloat} = _matmul!(C', B', A')
-
-_matmul!(C::AbstractVecOrMat, A::IKP, B::AbstractVecOrMat, alpha::Number, beta::Number) =
-    mul_vectrick!(C, A, B, alpha, beta)
-_matmul!(
-    C::AbstractVecOrMat{T},
-    A::IKP{T},
-    B::AbstractVecOrMat{T},
-    alpha::Number,
-    beta::Number,
-) where {T<:LinearAlgebra.BlasFloat} = mul_vectrick!(C, A, B, alpha, beta)
-_matmul!(C::AbstractVecOrMat, A::AbstractVecOrMat, B::IKP, alpha::Number, beta::Number) =
-    mul_vectrick!(C', B', A', alpha, beta)
-_matmul!(
-    C::AbstractVecOrMat{T},
-    A::AbstractVecOrMat{T},
-    B::IKP{T},
-    alpha::Number,
-    beta::Number,
-) where {T<:LinearAlgebra.BlasFloat} = mul_vectrick!(C', B', A', alpha, beta)
+for TC in [:AbstractVector, :AbstractMatrix]
+    @eval mul!(C::$TC, A::IKP, B::$TC) = mul_vectrick!(C, A, B)
+    @eval mul!(C::$TC, A::IKP, B::Adjoint{T,<:$TC{T}}) where {T} = mul_vectrick!(C, A, B)
+    @eval mul!(C::$TC, A::IKP, B::$TC, alpha::Number, beta::Number) =
+        mul_vectrick!(C, A, B, alpha, beta)
+
+    @eval _matmul!(C::$TC, A::IKP, B::$TC) = mul_vectrick!(C, A, B)
+    @eval _matmul!(
+        C::$TC{T},
+        A::IKP{T},
+        B::$TC{T},
+    ) where {T<:LinearAlgebra.BlasFloat} = mul_vectrick!(C, A, B)
+    @eval _matmul!(C::$TC, A::$TC, B::IKP) = _matmul!(C', B', A')
+    @eval _matmul!(
+        C::$TC{T},
+        A::$TC{T},
+        B::IKP{T},
+    ) where {T<:LinearAlgebra.BlasFloat} = _matmul!(C', B', A')
+
+    @eval _matmul!(C::$TC, A::IKP, B::$TC, alpha::Number, beta::Number) =
+        mul_vectrick!(C, A, B, alpha, beta)
+    @eval _matmul!(
+        C::$TC{T},
+        A::IKP{T},
+        B::$TC{T},
+        alpha::Number,
+        beta::Number,
+    ) where {T<:LinearAlgebra.BlasFloat} = mul_vectrick!(C, A, B, alpha, beta)
+    @eval _matmul!(C::$TC, A::$TC, B::IKP, alpha::Number, beta::Number) =
+        mul_vectrick!(C', B', A', alpha, beta)
+    @eval _matmul!(
+        C::$TC{T},
+        A::$TC{T},
+        B::IKP{T},
+        alpha::Number,
+        beta::Number,
+    ) where {T<:LinearAlgebra.BlasFloat} = mul_vectrick!(C', B', A', alpha, beta)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 9e948bd3d..ca6ec412b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -38,6 +38,9 @@ const GROUP = get(ENV, "GROUP", "All")
             @timedsafetestset "Smoothing" begin
                 include("smoothing.jl")
             end
+            @timedsafetestset "IsometricKroneckerProduct" begin
+                include("core/kronecker.jl")
+            end
         end
     end