diff --git a/test/diagonal.jl b/test/diagonal.jl
index e5fcaa430..0f67836dd 100644
--- a/test/diagonal.jl
+++ b/test/diagonal.jl
@@ -200,6 +200,16 @@ diagspacelist = ((ℂ^4)', ℂ[Z2Irrep](0 => 2, 1 => 3),
                 @test all(((s, t),) -> isapprox(s, t),
                           zip(values(LinearAlgebra.eigvals(D)),
                               values(LinearAlgebra.eigvals(t))))
+                D, W = @constinferred eig!(t)
+                @test D === t
+                @test W == one(t)
+                @test t * W ≈ W * D
+                D2, V2 = @constinferred eigh!(t2)
+                if T <: Real
+                    @test D2 === t2
+                end
+                @test V2 == one(t)
+                @test t2 * V2 ≈ V2 * D2
             end
             @testset "leftorth with $alg" for alg in (TensorKit.QR(), TensorKit.QL())
                 Q, R = @constinferred leftorth(t; alg=alg)
diff --git a/test/tensors.jl b/test/tensors.jl
index cd0071b2e..2b73d49bd 100644
--- a/test/tensors.jl
+++ b/test/tensors.jl
@@ -490,6 +490,11 @@ for V in spacelist
                         for (c, b) in s
                             @test b ≈ s′[c]
                         end
+                        s = LinearAlgebra.svdvals(t2')
+                        s′ = LinearAlgebra.diag(S')
+                        for (c, b) in s
+                            @test b ≈ s′[c]
+                        end
                     end
                     @testset "cond and rank" begin
                         t2 = permute(t, ((3, 4, 2), (1, 5)))
@@ -507,6 +512,10 @@ for V in spacelist
                         λmax = maximum(s -> maximum(abs, s), values(vals))
                         λmin = minimum(s -> minimum(abs, s), values(vals))
                         @test cond(t4) ≈ λmax / λmin
+                        vals = LinearAlgebra.eigvals(t4')
+                        λmax = maximum(s -> maximum(abs, s), values(vals))
+                        λmin = minimum(s -> minimum(abs, s), values(vals))
+                        @test cond(t4') ≈ λmax / λmin
                     end
                 end
                 @testset "empty tensor" begin