diff --git a/Project.toml b/Project.toml
index 0551a6e..8ff53c4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,6 +3,8 @@ uuid = "14197337-ba66-59df-a3e3-ca00e7dcff7a"
 version = "0.2.4"
 
 [deps]
+GenericSchur = "c145ed77-6b09-5dd9-b285-bf645a82121e"
+GenericSVD = "01680d73-4ee2-5a08-a1aa-533608c188bb"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -16,3 +18,5 @@ test = ["Quaternions", "Test"]
 
 [compat]
 julia = "1.3"
+GenericSchur = "0.4"
+GenericSVD = "0.3"
diff --git a/src/GenericLinearAlgebra.jl b/src/GenericLinearAlgebra.jl
index 2ab778b..f796da0 100644
--- a/src/GenericLinearAlgebra.jl
+++ b/src/GenericLinearAlgebra.jl
@@ -1,6 +1,7 @@
 module GenericLinearAlgebra
 
 import LinearAlgebra: mul!, ldiv!
+import GenericSVD, GenericSchur
 
 include("juliaBLAS.jl")
 include("lapack.jl")
diff --git a/src/eigenGeneral.jl b/src/eigenGeneral.jl
index f1f7018..9f98c38 100644
--- a/src/eigenGeneral.jl
+++ b/src/eigenGeneral.jl
@@ -36,29 +36,6 @@ function LinearAlgebra.ldiv!(H::HessenbergMatrix, B::AbstractVecOrMat)
     ldiv!(Triangular(Hd, :U), B)
 end
 
-# Hessenberg factorization
-struct HessenbergFactorization{T, S<:StridedMatrix,U} <: Factorization{T}
-    data::S
-    τ::Vector{U}
-end
-
-function _hessenberg!(A::StridedMatrix{T}) where T
-    n = LinearAlgebra.checksquare(A)
-    τ = Vector{Householder{T}}(undef, n - 1)
-    for i = 1:n - 1
-        xi = view(A, i + 1:n, i)
-        t  = LinearAlgebra.reflector!(xi)
-        H  = Householder{T,typeof(xi)}(view(xi, 2:n - i), t)
-        τ[i] = H
-        lmul!(H', view(A, i + 1:n, i + 1:n))
-        rmul!(view(A, :, i + 1:n), H)
-    end
-    return HessenbergFactorization{T, typeof(A), eltype(τ)}(A, τ)
-end
-LinearAlgebra.hessenberg!(A::StridedMatrix) = _hessenberg!(A)
-
-Base.size(H::HessenbergFactorization, args...) = size(H.data, args...)
-
 # Schur
 struct Schur{T,S<:StridedMatrix} <: Factorization{T}
     data::S
@@ -81,7 +58,7 @@ end
 
 # We currently absorb extra unsupported keywords in kwargs. These could e.g. be scale and permute. Do we want to check that these are false?
 function _schur!(
-    H::HessenbergFactorization{T};
+    H::GenericSchur.HessenbergArg{T};
     tol = eps(real(T)),
     debug = false,
     shiftmethod = :Francis,
@@ -91,7 +68,7 @@ function _schur!(
     n = size(H, 1)
     istart = 1
     iend = n
-    HH = H.data
+    HH = GenericSchur._getdata(H)
     τ = Rotation(Givens{T}[])
 
     # iteration count
@@ -166,7 +143,7 @@ function _schur!(
 
     return Schur{T,typeof(HH)}(HH, τ)
 end
-_schur!(A::StridedMatrix; kwargs...) = _schur!(_hessenberg!(A); kwargs...)
+_schur!(A::StridedMatrix; kwargs...) = _schur!(hessenberg!(A); kwargs...)
 LinearAlgebra.schur!(A::StridedMatrix; kwargs...) = _schur!(A; kwargs...)
 
 function singleShiftQR!(HH::StridedMatrix, τ::Rotation, shift::Number, istart::Integer, iend::Integer)
@@ -245,7 +222,7 @@ end
 
 _eigvals!(A::StridedMatrix; kwargs...)           = _eigvals!(_schur!(A; kwargs...))
 _eigvals!(H::HessenbergMatrix; kwargs...)        = _eigvals!(_schur!(H; kwargs...))
-_eigvals!(H::HessenbergFactorization; kwargs...) = _eigvals!(_schur!(H; kwargs...))
+_eigvals!(H::GenericSchur.HessenbergArg; kwargs...) = _eigvals!(_schur!(H; kwargs...))
 
 # Overload methods from LinearAlgebra to make them work generically
 if VERSION > v"1.2.0-DEV.0"
@@ -266,7 +243,7 @@ if VERSION > v"1.2.0-DEV.0"
         kwargs...) = LinearAlgebra.sorteig!(_eigvals!(H; kwargs...), sortby)
 
     LinearAlgebra.eigvals!(
-        H::HessenbergFactorization;
+        H::GenericSchur.HessenbergArg;
         sortby::Union{Function,Nothing}=LinearAlgebra.eigsortby,
         kwargs...) = LinearAlgebra.sorteig!(_eigvals!(H; kwargs...), sortby)
 else
@@ -280,7 +257,7 @@ else
 
     LinearAlgebra.eigvals!(H::HessenbergMatrix; kwargs...) = _eigvals!(H; kwargs...)
 
-    LinearAlgebra.eigvals!(H::HessenbergFactorization; kwargs...) = _eigvals!(H; kwargs...)
+    LinearAlgebra.eigvals!(H::GenericSchur.HessenbergArg; kwargs...) = _eigvals!(H; kwargs...)
 end
 
 # To compute the eigenvalue of the pseudo triangular Schur matrix we just return
diff --git a/src/qr.jl b/src/qr.jl
index b26df03..d2fb3d2 100644
--- a/src/qr.jl
+++ b/src/qr.jl
@@ -13,28 +13,6 @@ QR2(factors::AbstractMatrix{T}, τ::Vector{T}) where {T} = QR2{T,typeof(factors)
 
 size(F::QR2, i::Integer...) = size(F.factors, i...)
 
-# Similar to the definition in base but applies the reflector from the right
-@inline function reflectorApply!(A::StridedMatrix, x::AbstractVector, τ::Number) # apply conjugate transpose reflector from right.
-    m, n = size(A)
-    if length(x) != n
-        throw(DimensionMismatch("reflector must have same length as second dimension of matrix"))
-    end
-    @inbounds begin
-        for i in 1:m
-            Aiv = A[i, 1]
-            for j in 2:n
-                Aiv += A[i, j]*x[j]
-            end
-            Aiv = Aiv*τ
-            A[i, 1] -= Aiv
-            for j in 2:n
-                A[i, j] -= Aiv*x[j]'
-            end
-        end
-    end
-    return A
-end
-
 # FixMe! Consider how to represent Q
 
 # immutable Q{T,S<:QR2} <: AbstractMatrix{T}
diff --git a/src/svd.jl b/src/svd.jl
index 68944df..e6d206c 100644
--- a/src/svd.jl
+++ b/src/svd.jl
@@ -2,9 +2,6 @@ using LinearAlgebra
 
 import LinearAlgebra: mul!, rmul!
 
-lmul!(G::LinearAlgebra.Givens, ::Nothing) = nothing
-rmul!(::Nothing, G::LinearAlgebra.Givens) = nothing
-
 function svdvals2x2(d1, d2, e)
     d1sq = d1*d1
     d2sq = d2*d2