isposdef, and tests

also made `isapprox` a standalone testset,
because it's irrelevant to `istriu`, `issymmetric`, etc

Author: ZeppLu

stdlib/LinearAlgebra/src/uniformscaling.jl

@@ -81,6 +81,8 @@ istril(::UniformScaling) = true
 issymmetric(::UniformScaling) = true
 ishermitian(J::UniformScaling) = isreal(J.λ)
 
+isposdef(J::UniformScaling) = isreal(J.λ) && J.λ > 0
+
 (+)(J::UniformScaling, x::Number) = J.λ + x
 (+)(x::Number, J::UniformScaling) = x + J.λ
 (-)(J::UniformScaling, x::Number) = J.λ - x

stdlib/LinearAlgebra/test/uniformscaling.jl

@@ -88,13 +88,20 @@ end
     @test conj(UniformScaling(1.0+1.0im))::UniformScaling{Complex{Float64}} == UniformScaling(1.0-1.0im)
 end
 
-@testset "istriu, istril, issymmetric, ishermitian, isapprox" begin
+@testset "istriu, istril, issymmetric, ishermitian, isposdef" begin
     @test istriu(I)
     @test istril(I)
     @test issymmetric(I)
     @test issymmetric(UniformScaling(complex(1.0,1.0)))
     @test ishermitian(I)
     @test !ishermitian(UniformScaling(complex(1.0,1.0)))
+    @test isposdef(UniformScaling(rand()))
+    @test !isposdef(UniformScaling(-rand()))
+    @test !isposdef(UniformScaling(randn(ComplexF64)))
+    @test !isposdef(UniformScaling(NaN))
+end
+
+@testset "isapprox" begin
     @test UniformScaling(4.00000000000001) ≈ UniformScaling(4.0)
     @test UniformScaling(4.32) ≈ UniformScaling(4.3) rtol=0.1 atol=0.01
     @test UniformScaling(4.32) ≈ 4.3 * [1 0; 0 1] rtol=0.1 atol=0.01