diff --git a/ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl b/ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl
index e4637875..14c63a4e 100644
--- a/ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl
+++ b/ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl
@@ -1,7 +1,7 @@
 module MatrixAlgebraKitGenericLinearAlgebraExt
 
 using MatrixAlgebraKit
-using MatrixAlgebraKit: sign_safe, check_input, diagview, gaugefix!, default_fixgauge
+using MatrixAlgebraKit: sign_safe, check_input, diagview, gaugefix!, one!, default_fixgauge
 using GenericLinearAlgebra: svd!, svdvals!, eigen!, eigvals!, Hermitian, qr!
 using LinearAlgebra: I, Diagonal, lmul!
 
@@ -72,6 +72,11 @@ function MatrixAlgebraKit.qr_compact!(A::AbstractMatrix, QR, alg::GLA_Householde
     return _gla_householder_qr!(A, Q, R; alg.kwargs...)
 end
 
+function MatrixAlgebraKit.qr_null!(A::AbstractMatrix, N, alg::GLA_HouseholderQR)
+    check_input(qr_null!, A, N, alg)
+    return _gla_householder_qr_null!(A, N; alg.kwargs...)
+end
+
 function _gla_householder_qr!(A::AbstractMatrix, Q, R; positive = false, blocksize = 1, pivoted = false)
     pivoted && throw(ArgumentError("Only pivoted = false implemented for GLA_HouseholderQR."))
     (blocksize == 1) || throw(ArgumentError("Only blocksize = 1 implemented for GLA_HouseholderQR."))
@@ -109,6 +114,21 @@ function _gla_householder_qr!(A::AbstractMatrix, Q, R; positive = false, blocksi
     return Q, R
 end
 
+function _gla_householder_qr_null!(
+        A::AbstractMatrix, N::AbstractMatrix;
+        positive = false, blocksize = 1, pivoted = false
+    )
+    pivoted && throw(ArgumentError("Only pivoted = false implemented for GLA_HouseholderQR."))
+    (blocksize == 1) || throw(ArgumentError("Only blocksize = 1 implemented for GLA_HouseholderQR."))
+    m, n = size(A)
+    minmn = min(m, n)
+    fill!(N, zero(eltype(N)))
+    one!(view(N, (minmn + 1):m, 1:(m - minmn)))
+    Q̃, = qr!(A)
+    lmul!(Q̃, N)
+    return N
+end
+
 function MatrixAlgebraKit.default_lq_algorithm(::Type{T}; kwargs...) where {T <: StridedMatrix{<:Union{Float16, ComplexF16, BigFloat, Complex{BigFloat}}}}
     return MatrixAlgebraKit.LQViaTransposedQR(GLA_HouseholderQR(; kwargs...))
 end
diff --git a/test/lq.jl b/test/lq.jl
index 2f34e846..4da1fc7a 100644
--- a/test/lq.jl
+++ b/test/lq.jl
@@ -51,9 +51,9 @@ for T in (BLASFloats..., GenericFloats...), n in (37, m, 63)
             )
             TestSuite.test_lq_algs(T, (m, n), LAPACK_LQ_ALGS)
         elseif T ∈ GenericFloats
-            TestSuite.test_lq(T, (m, n); test_null = false, test_pivoted = false, test_blocksize = false)
+            TestSuite.test_lq(T, (m, n); test_null = true, test_pivoted = false, test_blocksize = false)
             GLA_LQ_ALGS = (LQViaTransposedQR(GLA_HouseholderQR()),)
-            TestSuite.test_lq_algs(T, (m, n), GLA_LQ_ALGS; test_null = false)
+            TestSuite.test_lq_algs(T, (m, n), GLA_LQ_ALGS; test_null = true)
         end
         if m == n
             AT = Diagonal{T, Vector{T}}
diff --git a/test/qr.jl b/test/qr.jl
index 8b420fc6..3131349a 100644
--- a/test/qr.jl
+++ b/test/qr.jl
@@ -50,7 +50,7 @@ for T in (BLASFloats..., GenericFloats...), n in (37, m, 63)
             )
             TestSuite.test_qr_algs(T, (m, n), LAPACK_QR_ALGS)
         elseif T ∈ GenericFloats
-            TestSuite.test_qr(T, (m, n); test_null = false, test_pivoted = false, test_blocksize = false)
+            TestSuite.test_qr(T, (m, n); test_null = true, test_pivoted = false, test_blocksize = false)
             GLA_QR_ALGS = (GLA_HouseholderQR(),)
             TestSuite.test_qr_algs(T, (m, n), GLA_QR_ALGS; test_null = false)
         end