Default uplo in symmetric/hermitian (#52605)

This makes the function signatures match the respective docstrings, as
well as that of `Symmetric/Hermitian`.

stdlib/LinearAlgebra/src/symmetric.jl

@@ -73,8 +73,8 @@ If a symmetric view of a matrix is to be constructed of which the elements are n
 matrices nor numbers, an appropriate method of `symmetric` has to be implemented. In that
 case, `symmetric_type` has to be implemented, too.
 """
-symmetric(A::AbstractMatrix, uplo::Symbol) = Symmetric(A, uplo)
-symmetric(A::Number, ::Symbol) = A
+symmetric(A::AbstractMatrix, uplo::Symbol=:U) = Symmetric(A, uplo)
+symmetric(A::Number, ::Symbol=:U) = A
 
 """
     symmetric_type(T::Type)
@@ -164,8 +164,8 @@ If a hermitian view of a matrix is to be constructed of which the elements are n
 matrices nor numbers, an appropriate method of `hermitian` has to be implemented. In that
 case, `hermitian_type` has to be implemented, too.
 """
-hermitian(A::AbstractMatrix, uplo::Symbol) = Hermitian(A, uplo)
-hermitian(A::Number, ::Symbol) = convert(typeof(A), real(A))
+hermitian(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(A, uplo)
+hermitian(A::Number, ::Symbol=:U) = convert(typeof(A), real(A))
 
 """
     hermitian_type(T::Type)

stdlib/LinearAlgebra/test/symmetric.jl

@@ -729,9 +729,9 @@ end
 end
 
 @testset "symmetric()/hermitian() for Numbers" begin
-    @test LinearAlgebra.symmetric(1, :U) == 1
+    @test LinearAlgebra.symmetric(1) == LinearAlgebra.symmetric(1, :U) == 1
     @test LinearAlgebra.symmetric_type(Int) == Int
-    @test LinearAlgebra.hermitian(1, :U) == 1
+    @test LinearAlgebra.hermitian(1) == LinearAlgebra.hermitian(1, :U) == 1
     @test LinearAlgebra.hermitian_type(Int) == Int
 end
 
@@ -902,6 +902,14 @@ end
     end
 end
 
+@testset "symmetric/hermitian for matrices" begin
+    A = [1 2; 3 4]
+    @test LinearAlgebra.symmetric(A) === Symmetric(A)
+    @test LinearAlgebra.symmetric(A, :L) === Symmetric(A, :L)
+    @test LinearAlgebra.hermitian(A) === Hermitian(A)
+    @test LinearAlgebra.hermitian(A, :L) === Hermitian(A, :L)
+end
+
 @testset "custom axes" begin
     SZA = SizedArrays.SizedArray{(2,2)}([1 2; 3 4])
     for T in (Symmetric, Hermitian)