diff --git a/stdlib/LinearAlgebra/src/dense.jl b/stdlib/LinearAlgebra/src/dense.jl
index aacc5479bfa9d..d8f2513f5bfc8 100644
--- a/stdlib/LinearAlgebra/src/dense.jl
+++ b/stdlib/LinearAlgebra/src/dense.jl
@@ -110,6 +110,7 @@ norm2(x::Union{Array{T},StridedVector{T}}) where {T<:BlasFloat} =
 # Conservative assessment of types that have zero(T) defined for themselves
 haszero(::Type) = false
 haszero(::Type{T}) where {T<:Number} = isconcretetype(T)
+haszero(::Type{Union{Missing,T}}) where {T<:Number} = haszero(T)
 @propagate_inbounds _zero(M::AbstractArray{T}, inds...) where {T} = haszero(T) ? zero(T) : zero(M[inds...])
 
 """
diff --git a/stdlib/LinearAlgebra/test/triangular.jl b/stdlib/LinearAlgebra/test/triangular.jl
index ec9a3079e2643..0c358491c43c7 100644
--- a/stdlib/LinearAlgebra/test/triangular.jl
+++ b/stdlib/LinearAlgebra/test/triangular.jl
@@ -1284,6 +1284,14 @@ end
             @test istril(U, k) == istril(A, k)
         end
     end
+
+    @testset "Union eltype" begin
+        M = Matrix{Union{Int,Missing}}(missing,2,2)
+        U = triu(M)
+        @test iszero(U[2,1])
+        U = tril(M)
+        @test iszero(U[1,2])
+    end
 end
 
 @testset "indexing with a BandIndex" begin