From 3071f34b16059ea7279c2af5694f902155d0806e Mon Sep 17 00:00:00 2001
From: Sebastian Stock <42280794+sostock@users.noreply.github.com>
Date: Tue, 23 Mar 2021 08:53:54 +0100
Subject: [PATCH] Preserve `Symmetric`/`Hermitian` shape in more cases (#40126)

---
 stdlib/LinearAlgebra/src/symmetric.jl  |  4 ++++
 stdlib/LinearAlgebra/test/symmetric.jl | 25 +++++++++++++++++++++++++
 2 files changed, 29 insertions(+)

diff --git a/stdlib/LinearAlgebra/src/symmetric.jl b/stdlib/LinearAlgebra/src/symmetric.jl
index 8f1073817b71d..e206cfe7178d3 100644
--- a/stdlib/LinearAlgebra/src/symmetric.jl
+++ b/stdlib/LinearAlgebra/src/symmetric.jl
@@ -482,6 +482,10 @@ for f in (:+, :-)
     @eval begin
         $f(A::Hermitian, B::Symmetric{<:Real}) = $f(A, Hermitian(parent(B), sym_uplo(B.uplo)))
         $f(A::Symmetric{<:Real}, B::Hermitian) = $f(Hermitian(parent(A), sym_uplo(A.uplo)), B)
+        $f(A::SymTridiagonal, B::Symmetric) = Symmetric($f(A, B.data), sym_uplo(B.uplo))
+        $f(A::Symmetric, B::SymTridiagonal) = Symmetric($f(A.data, B), sym_uplo(A.uplo))
+        $f(A::SymTridiagonal{<:Real}, B::Hermitian) = Hermitian($f(A, B.data), sym_uplo(B.uplo))
+        $f(A::Hermitian, B::SymTridiagonal{<:Real}) = Hermitian($f(A.data, B), sym_uplo(A.uplo))
     end
 end
 
diff --git a/stdlib/LinearAlgebra/test/symmetric.jl b/stdlib/LinearAlgebra/test/symmetric.jl
index 7d99dd32889fd..d23eecb5be46e 100644
--- a/stdlib/LinearAlgebra/test/symmetric.jl
+++ b/stdlib/LinearAlgebra/test/symmetric.jl
@@ -727,4 +727,29 @@ end
     end
 end
 
+@testset "Addition/subtraction with SymTridiagonal" begin
+    TR = SymTridiagonal(randn(Float64,5), randn(Float64,4))
+    TC = SymTridiagonal(randn(ComplexF64,5), randn(ComplexF64,4))
+    SR = Symmetric(randn(Float64,5,5))
+    SC = Symmetric(randn(ComplexF64,5,5))
+    HR = Hermitian(randn(Float64,5,5))
+    HC = Hermitian(randn(ComplexF64,5,5))
+    for op = (+,-)
+        for T = (TR, TC), S = (SR, SC)
+            @test op(T, S) == op(Array(T), S)
+            @test op(S, T) == op(S, Array(T))
+            @test op(T, S) isa Symmetric
+            @test op(S, T) isa Symmetric
+        end
+        for H = (HR, HC)
+            for T = (TR, TC)
+                @test op(T, H) == op(Array(T), H)
+                @test op(H, T) == op(H, Array(T))
+            end
+            @test op(TR, H) isa Hermitian
+            @test op(H, TR) isa Hermitian
+        end
+    end
+end
+
 end # module TestSymmetric