diff --git a/stdlib/SparseArrays/src/higherorderfns.jl b/stdlib/SparseArrays/src/higherorderfns.jl
index 63d318af434f9..66ab8b3f60e52 100644
--- a/stdlib/SparseArrays/src/higherorderfns.jl
+++ b/stdlib/SparseArrays/src/higherorderfns.jl
@@ -8,7 +8,8 @@ import Base: map, map!, broadcast, copy, copyto!
 
 using Base: front, tail, to_shape
 using ..SparseArrays: SparseVector, SparseMatrixCSC, AbstractSparseVector,
-                      AbstractSparseMatrix, AbstractSparseArray, indtype, nnz, nzrange
+                      AbstractSparseMatrix, AbstractSparseArray, indtype, nnz, nzrange,
+                      SparseVectorUnion, AdjOrTransSparseVectorUnion, nonzeroinds, nonzeros
 using Base.Broadcast: BroadcastStyle, Broadcasted, flatten
 using LinearAlgebra
 
@@ -92,6 +93,9 @@ is_supported_sparse_broadcast(t::Union{Transpose, Adjoint}, rest...) = is_suppor
 is_supported_sparse_broadcast(x, rest...) = axes(x) === () && is_supported_sparse_broadcast(rest...)
 is_supported_sparse_broadcast(x::Ref, rest...) = is_supported_sparse_broadcast(rest...)
 
+can_skip_sparsification(f, rest...) = false
+can_skip_sparsification(::typeof(*), ::SparseVectorUnion, ::AdjOrTransSparseVectorUnion) = true
+
 # Dispatch on broadcast operations by number of arguments
 const Broadcasted0{Style<:Union{Nothing,BroadcastStyle},Axes,F} =
     Broadcasted{Style,Axes,F,Tuple{}}
@@ -810,6 +814,48 @@ end
 _finishempty!(C::SparseVector) = C
 _finishempty!(C::SparseMatrixCSC) = (fill!(C.colptr, 1); C)
 
+# special case - vector outer product
+_copy(f::typeof(*), x::SparseVectorUnion, y::AdjOrTransSparseVectorUnion) = _outer(x, y)
+@inline _outer(x::SparseVectorUnion, y::Adjoint) = return _outer(conj, x, parent(y))
+@inline _outer(x::SparseVectorUnion, y::Transpose) = return _outer(identity, x, parent(y))
+function _outer(trans::Tf, x, y) where Tf
+    nx = length(x)
+    ny = length(y)
+    rowvalx = nonzeroinds(x)
+    rowvaly = nonzeroinds(y)
+    nzvalsx = nonzeros(x)
+    nzvalsy = nonzeros(y)
+    nnzx = length(nzvalsx)
+    nnzy = length(nzvalsy)
+
+    nnzC = nnzx * nnzy
+    Tv = typeof(oneunit(eltype(x)) * oneunit(eltype(y)))
+    Ti = promote_type(indtype(x), indtype(y))
+    colptrC = zeros(Ti, ny + 1)
+    rowvalC = Vector{Ti}(undef, nnzC)
+    nzvalsC = Vector{Tv}(undef, nnzC)
+
+    idx = 0
+    @inbounds colptrC[1] = 1
+    @inbounds for jj = 1:nnzy
+        yval = nzvalsy[jj]
+        iszero(yval) && continue
+        col = rowvaly[jj]
+        yval = trans(yval)
+
+        for ii = 1:nnzx
+            xval = nzvalsx[ii]
+            iszero(xval) && continue
+            idx += 1
+            colptrC[col+1] += 1
+            rowvalC[idx] = rowvalx[ii]
+            nzvalsC[idx] = xval * yval
+        end
+    end
+    cumsum!(colptrC, colptrC)
+
+    return SparseMatrixCSC(nx, ny, colptrC, rowvalC, nzvalsC)
+end
 
 # (9) _broadcast_zeropres!/_broadcast_notzeropres! for more than two (input) sparse vectors/matrices
 function _broadcast_zeropres!(f::Tf, C::SparseVecOrMat, As::Vararg{SparseVecOrMat,N}) where {Tf,N}
@@ -1079,8 +1125,10 @@ broadcast(f::Tf, A::SparseMatrixCSC, ::Type{T}) where {Tf,T} = broadcast(x -> f(
 
 function copy(bc::Broadcasted{PromoteToSparse})
     bcf = flatten(bc)
-    if is_supported_sparse_broadcast(bcf.args...)
-        broadcast(bcf.f, map(_sparsifystructured, bcf.args)...)
+    if can_skip_sparsification(bcf.f, bcf.args...)
+        return _copy(bcf.f, bcf.args...)
+    elseif is_supported_sparse_broadcast(bcf.args...)
+        return _copy(bcf.f, map(_sparsifystructured, bcf.args)...)
     else
         return copy(convert(Broadcasted{Broadcast.DefaultArrayStyle{length(axes(bc))}}, bc))
     end
diff --git a/stdlib/SparseArrays/src/linalg.jl b/stdlib/SparseArrays/src/linalg.jl
index 0c7fea10b32ac..c0d352bafcaa7 100644
--- a/stdlib/SparseArrays/src/linalg.jl
+++ b/stdlib/SparseArrays/src/linalg.jl
@@ -1198,6 +1198,9 @@ kron(x::SparseVector, A::SparseMatrixCSC) = kron(SparseMatrixCSC(x), A)
 kron(A::Union{SparseVector,SparseMatrixCSC}, B::VecOrMat) = kron(A, sparse(B))
 kron(A::VecOrMat, B::Union{SparseVector,SparseMatrixCSC}) = kron(sparse(A), B)
 
+# sparse outer product
+kron(A::SparseVectorUnion, B::AdjOrTransSparseVectorUnion) = A .* B
+
 ## det, inv, cond
 
 inv(A::SparseMatrixCSC) = error("The inverse of a sparse matrix can often be dense and can cause the computer to run out of memory. If you are sure you have enough memory, please convert your matrix to a dense matrix.")
diff --git a/stdlib/SparseArrays/src/sparsevector.jl b/stdlib/SparseArrays/src/sparsevector.jl
index ea46ebd213c2d..305e93ee1a0bb 100644
--- a/stdlib/SparseArrays/src/sparsevector.jl
+++ b/stdlib/SparseArrays/src/sparsevector.jl
@@ -34,6 +34,7 @@ SparseVector(n::Integer, nzind::Vector{Ti}, nzval::Vector{Tv}) where {Tv,Ti} =
 # union of such a view and a SparseVector so we define an alias for such a union as well
 const SparseColumnView{T}  = SubArray{T,1,<:SparseMatrixCSC,Tuple{Base.Slice{Base.OneTo{Int}},Int},false}
 const SparseVectorUnion{T} = Union{SparseVector{T}, SparseColumnView{T}}
+const AdjOrTransSparseVectorUnion{T} = LinearAlgebra.AdjOrTrans{T, <:SparseVectorUnion{T}}
 
 ### Basic properties
 
@@ -58,6 +59,11 @@ function nonzeroinds(x::SparseColumnView)
     return y
 end
 
+indtype(x::SparseColumnView) = indtype(parent(x))
+function nnz(x::SparseColumnView)
+    rowidx, colidx = parentindices(x)
+    return length(nzrange(parent(x), colidx))
+end
 
 ## similar
 #
diff --git a/stdlib/SparseArrays/test/higherorderfns.jl b/stdlib/SparseArrays/test/higherorderfns.jl
index 5b1423582f0d5..5d353f431cb38 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 dfb9aa9a284fa..1c8bf76e166e5 100644
--- a/stdlib/SparseArrays/test/sparse.jl
+++ b/stdlib/SparseArrays/test/sparse.jl
@@ -352,6 +352,7 @@ 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
@@ -370,6 +371,11 @@ 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)