diff --git a/stdlib/SparseArrays/test/higherorderfns.jl b/stdlib/SparseArrays/test/higherorderfns.jl
index 5b1423582f0d54..5d353f431cb382 100644
--- a/stdlib/SparseArrays/test/higherorderfns.jl
+++ b/stdlib/SparseArrays/test/higherorderfns.jl
@@ -656,4 +656,19 @@ using SparseArrays.HigherOrderFns: SparseVecStyle
     @test occursin("no method matching _copy(::typeof(rand))", sprint(showerror, err))
 end
 
+@testset "Sparse outer product, for type $T and vector $op" for
+         op in (transpose, adjoint),
+         T in (Float64, ComplexF64)
+    m, n, p = 100, 250, 0.1
+    A = sprand(T, m, n, p)
+    a, b = view(A, :, 1), sprand(T, m, p)
+    av, bv = Vector(a), Vector(b)
+    v = @inferred a .* op(b)
+    w = @inferred b .* op(a)
+    @test issparse(v)
+    @test issparse(w)
+    @test v == av .* op(bv)
+    @test w == bv .* op(av)
+end
+
 end # module
diff --git a/stdlib/SparseArrays/test/sparse.jl b/stdlib/SparseArrays/test/sparse.jl
index a37034a9137379..e28ca1085cb37d 100644
--- a/stdlib/SparseArrays/test/sparse.jl
+++ b/stdlib/SparseArrays/test/sparse.jl
@@ -343,6 +343,7 @@ end
     for (m,n) in ((5,10), (13,8), (14,10))
         a = sprand(m, 5, 0.4); a_d = Matrix(a)
         b = sprand(n, 6, 0.3); b_d = Matrix(b)
+        v = view(a, :, 1); v_d = Vector(v)
         x = sprand(m, 0.4); x_d = Vector(x)
         y = sprand(n, 0.3); y_d = Vector(y)
         # mat ⊗ mat
@@ -361,6 +362,11 @@ end
         @test Array(kron(x, b)) == kron(x_d, b_d)
         @test Array(kron(x_d, b)) == kron(x_d, b_d)
         @test Array(kron(x, b_d)) == kron(x_d, b_d)
+        # vec ⊗ vec'
+        @test issparse(kron(v, y'))
+        @test issparse(kron(x, y'))
+        @test Array(kron(v, y')) == kron(v_d, y_d')
+        @test Array(kron(x, y')) == kron(x_d, y_d')
         # test different types
         z = convert(SparseVector{Float16, Int8}, y); z_d = Vector(z)
         @test Vector(kron(x, z)) == kron(x_d, z_d)