diff --git a/src/linalg.jl b/src/linalg.jl
index d3bf24f3..9b584990 100644
--- a/src/linalg.jl
+++ b/src/linalg.jl
@@ -359,6 +359,11 @@ end
 *(A::SparseOrTri, B::AdjOrTrans{<:Any,<:AbstractSparseMatrixCSC}) = spmatmul(A, copy(B))
 *(A::AdjOrTrans{<:Any,<:AbstractSparseMatrixCSC}, B::SparseOrTri) = spmatmul(copy(A), B)
 *(A::AdjOrTrans{<:Any,<:AbstractSparseMatrixCSC}, B::AdjOrTrans{<:Any,<:AbstractSparseMatrixCSC}) = spmatmul(copy(A), copy(B))
+# a symmetric/Hermitian sparse factor is materialized, which is O(nnz) like the copies above
+*(A::SparseMatrixCSCSymmHerm, B::Union{SparseOrTri,AdjOrTrans{<:Any,<:AbstractSparseMatrixCSC}}) = sparse(A) * B
+*(A::Union{SparseOrTri,AdjOrTrans{<:Any,<:AbstractSparseMatrixCSC}}, B::SparseMatrixCSCSymmHerm) = A * sparse(B)
+*(A::SparseMatrixCSCSymmHerm, B::SparseMatrixCSCSymmHerm) = sparse(A) * sparse(B)
+*(A::SparseMatrixCSCSymmHerm, x::SparseVectorOrView) = sparse(A) * x
 
 (*)(Da::Diagonal, A::Union{SparseMatrixCSCOrView, AdjOrTrans{<:Any,<:AbstractSparseMatrixCSC}}, Db::Diagonal) = Da * (A * Db)
 function (*)(Da::Diagonal, A::SparseMatrixCSC, Db::Diagonal)
diff --git a/test/linalg_products.jl b/test/linalg_products.jl
index 20103eae..76227f2e 100644
--- a/test/linalg_products.jl
+++ b/test/linalg_products.jl
@@ -93,6 +93,30 @@ end
     end
 end
 
+@testset "symmetric/Hermitian sparse times sparse" begin
+    n = 10
+    @testset "$T" for T in (Float64, ComplexF64)
+        A = sprandn(T, n, n, 0.3); B = sprandn(T, n, n, 0.3)
+        for S in (Symmetric(A), Hermitian(A, :L), Symmetric(view(A, :, 1:n)))
+            for X in (B, B', transpose(B), UpperTriangular(B), view(B, :, 1:n), Hermitian(B), Symmetric(B, :L))
+                @test (S * X)::SparseMatrixCSC ≈ Matrix(S) * Matrix(X)
+                @test (X * S)::SparseMatrixCSC ≈ Matrix(X) * Matrix(S)
+            end
+            for x in (sprandn(T, n, 0.5), view(B, :, 2))
+                @test (S * x)::SparseVector ≈ Matrix(S) * Vector(x)
+            end
+        end
+    end
+    # one multiplication per pair of matching stored entries, not per element
+    P = mulcount_sparse(sparse(1.0I, n, n))
+    for f in (() -> Symmetric(P) * P, () -> P * Symmetric(P), () -> P' * Symmetric(P),
+              () -> UpperTriangular(P) * Symmetric(P), () -> Symmetric(P) * Symmetric(P, :L))
+        @test mulcount(f) == n
+    end
+    x = sparsevec(fill(MulCount(1.0), n))
+    @test mulcount(() -> Symmetric(P) * x) == mulcount(() -> P * x)
+end
+
 @testset "Adding sparse-backed SymTridiagonal (#46355)" begin
     a = SymTridiagonal(sparsevec(Int[1]), sparsevec(Int[]))
     @test a + a == Matrix(a) + Matrix(a)