From 6613008ffdbd6e7ade81032e4647423ab1c8e48b Mon Sep 17 00:00:00 2001
From: Lea Kapelevich <leakapelevich@gmail.com>
Date: Sun, 28 Mar 2021 20:28:56 -0400
Subject: [PATCH 1/4] define dot between AbstractMatrix and UniformScaling

---
 stdlib/LinearAlgebra/src/uniformscaling.jl  | 3 +++
 stdlib/LinearAlgebra/test/uniformscaling.jl | 8 ++++++++
 2 files changed, 11 insertions(+)

diff --git a/stdlib/LinearAlgebra/src/uniformscaling.jl b/stdlib/LinearAlgebra/src/uniformscaling.jl
index c59871e0641ef..963f38279ff00 100644
--- a/stdlib/LinearAlgebra/src/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/src/uniformscaling.jl
@@ -480,6 +480,9 @@ Array(s::UniformScaling, dims::Dims{2}) = Matrix(s, dims)
 Diagonal{T}(s::UniformScaling, m::Integer) where {T} = Diagonal{T}(fill(T(s.λ), m))
 Diagonal(s::UniformScaling, m::Integer) = Diagonal{eltype(s)}(s, m)
 
+dot(A::AbstractMatrix, J::UniformScaling) = tr(A)*J.λ
+dot(J::UniformScaling, A::AbstractMatrix) = J.λ*tr(A)
+
 dot(x::AbstractVector, J::UniformScaling, y::AbstractVector) = dot(x, J.λ, y)
 dot(x::AbstractVector, a::Number, y::AbstractVector) = sum(t -> dot(t[1], a, t[2]), zip(x, y))
 dot(x::AbstractVector, a::Union{Real,Complex}, y::AbstractVector) = a*dot(x, y)
diff --git a/stdlib/LinearAlgebra/test/uniformscaling.jl b/stdlib/LinearAlgebra/test/uniformscaling.jl
index 27f6641657e81..7fd2c168c0a87 100644
--- a/stdlib/LinearAlgebra/test/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/test/uniformscaling.jl
@@ -460,6 +460,14 @@ end
     @test I(3) == [1 0 0; 0 1 0; 0 0 1]
 end
 
+@testset "dot" begin
+    A = rand(-10:10, 3, 3)
+    λ = rand(-10:10)
+    J = UniformScaling(λ)
+    @test dot(A, J) ≈ dot(J, A)
+    @test dot(A, J) ≈ tr(λ * A)
+end
+
 @testset "generalized dot" begin
     x = rand(-10:10, 3)
     y = rand(-10:10, 3)

From a3dd3512baa98a5728dcb37e5efd16383ef26fc5 Mon Sep 17 00:00:00 2001
From: Lea Kapelevich <leakapelevich@gmail.com>
Date: Sun, 28 Mar 2021 20:32:00 -0400
Subject: [PATCH 2/4] fix equality check

---
 stdlib/LinearAlgebra/test/uniformscaling.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/stdlib/LinearAlgebra/test/uniformscaling.jl b/stdlib/LinearAlgebra/test/uniformscaling.jl
index 7fd2c168c0a87..4895a9c7aa2d0 100644
--- a/stdlib/LinearAlgebra/test/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/test/uniformscaling.jl
@@ -464,8 +464,8 @@ end
     A = rand(-10:10, 3, 3)
     λ = rand(-10:10)
     J = UniformScaling(λ)
-    @test dot(A, J) ≈ dot(J, A)
-    @test dot(A, J) ≈ tr(λ * A)
+    @test dot(A, J) == dot(J, A)
+    @test dot(A, J) == tr(λ * A)
 end
 
 @testset "generalized dot" begin

From bb8f7d4cd429ea98e44cd3841d899571557863aa Mon Sep 17 00:00:00 2001
From: Lea Kapelevich <leakapelevich@gmail.com>
Date: Tue, 30 Mar 2021 08:18:04 -0400
Subject: [PATCH 3/4] fix for complex

---
 stdlib/LinearAlgebra/src/uniformscaling.jl  |  4 ++--
 stdlib/LinearAlgebra/test/uniformscaling.jl | 14 ++++++++++----
 2 files changed, 12 insertions(+), 6 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/uniformscaling.jl b/stdlib/LinearAlgebra/src/uniformscaling.jl
index 963f38279ff00..edcf12796550d 100644
--- a/stdlib/LinearAlgebra/src/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/src/uniformscaling.jl
@@ -480,8 +480,8 @@ Array(s::UniformScaling, dims::Dims{2}) = Matrix(s, dims)
 Diagonal{T}(s::UniformScaling, m::Integer) where {T} = Diagonal{T}(fill(T(s.λ), m))
 Diagonal(s::UniformScaling, m::Integer) = Diagonal{eltype(s)}(s, m)
 
-dot(A::AbstractMatrix, J::UniformScaling) = tr(A)*J.λ
-dot(J::UniformScaling, A::AbstractMatrix) = J.λ*tr(A)
+dot(A::AbstractMatrix, J::UniformScaling) = dot(tr(A), J.λ)
+dot(J::UniformScaling, A::AbstractMatrix) = dot(J.λ, tr(A))
 
 dot(x::AbstractVector, J::UniformScaling, y::AbstractVector) = dot(x, J.λ, y)
 dot(x::AbstractVector, a::Number, y::AbstractVector) = sum(t -> dot(t[1], a, t[2]), zip(x, y))
diff --git a/stdlib/LinearAlgebra/test/uniformscaling.jl b/stdlib/LinearAlgebra/test/uniformscaling.jl
index 4895a9c7aa2d0..ab0d503649898 100644
--- a/stdlib/LinearAlgebra/test/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/test/uniformscaling.jl
@@ -461,11 +461,17 @@ end
 end
 
 @testset "dot" begin
-    A = rand(-10:10, 3, 3)
-    λ = rand(-10:10)
+    A = randn(3, 3)
+    λ = randn()
+    J = UniformScaling(λ)
+    @test dot(A, J) ≈ dot(J, A)
+    @test dot(A, J) ≈ tr(A' * J)
+
+    A = rand(ComplexF64, 3, 3)
+    λ = randn() + im * randn()
     J = UniformScaling(λ)
-    @test dot(A, J) == dot(J, A)
-    @test dot(A, J) == tr(λ * A)
+    @test dot(A, J) ≈ conj(dot(J, A))
+    @test dot(A, J) ≈ tr(A' * J)
 end
 
 @testset "generalized dot" begin

From 37542fac44b2f3bf1e877726936180afc047e4f0 Mon Sep 17 00:00:00 2001
From: Lea Kapelevich <leakapelevich@gmail.com>
Date: Wed, 7 Apr 2021 10:11:57 -0400
Subject: [PATCH 4/4] add news entry

---
 NEWS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/NEWS.md b/NEWS.md
index 140da486c30bf..855da0305ba5d 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -74,6 +74,7 @@ Standard library changes
 * OpenBLAS is updated to 0.3.13. ([#39216])
 * SuiteSparse is updated to 5.8.1. ([#39455])
 * `cis(A)` now supports matrix arguments ([#40194]).
+* `dot` now supports `UniformScaling` with `AbstractMatrix` ([#40250]).
 
 #### Markdown