diff --git a/stdlib/LinearAlgebra/src/uniformscaling.jl b/stdlib/LinearAlgebra/src/uniformscaling.jl
index fc082764c6f4f..88ef64c2fe104 100644
--- a/stdlib/LinearAlgebra/src/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/src/uniformscaling.jl
@@ -97,6 +97,12 @@ isposdef(J::UniformScaling) = isposdef(J.λ)
 (-)(J::UniformScaling, B::BitArray{2})      = J - Array(B)
 (-)(A::AbstractMatrix, J::UniformScaling)   = A + (-J)
 
+# Promotion of scalar to uniform scaling under addition/subtraction
+(+)(a::Number, A::AbstractMatrix) = UniformScaling(a) + A
+(+)(A::AbstractMatrix, a::Number) = A + UniformScaling(a)
+(-)(a::Number, A::AbstractMatrix) = UniformScaling(a) - A
+(-)(A::AbstractMatrix, a::Number) = A - UniformScaling(a)
+
 # Unit{Lower/Upper}Triangular matrices become {Lower/Upper}Triangular under
 # addition with a UniformScaling
 for (t1, t2) in ((:UnitUpperTriangular, :UpperTriangular),
diff --git a/stdlib/LinearAlgebra/test/uniformscaling.jl b/stdlib/LinearAlgebra/test/uniformscaling.jl
index 887162d03dc20..67d7b001f2c9e 100644
--- a/stdlib/LinearAlgebra/test/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/test/uniformscaling.jl
@@ -64,6 +64,16 @@ end
     @test UniformScaling(α)/α == UniformScaling(1.0)
 end
 
+@testset "conversion of Number" begin
+    α = randn()
+    J = UniformScaling(α)
+    A = randn(2, 2)
+    @test α + A == J + A
+    @test A + α == A + J
+    @test α - A == J - A
+    @test A - α == A - J
+end
+
 @testset "det and logdet" begin
     @test det(I) === true
     @test det(1.0I) === 1.0