add det(Symmetric)=det(full(Symmetric))

closes #13088

Author: alyst

base/linalg/symmetric.jl

@@ -55,6 +55,7 @@ function transpose(A::Hermitian)
 end
 ctranspose(A::Hermitian) = A
 trace(A::Hermitian) = real(trace(A.data))
+det(A::HermOrSym) = det(full(A))
 
 #tril/triu
 function tril(A::Hermitian, k::Integer=0)

test/linalg/symmetric.jl

@@ -10,19 +10,26 @@ for σ in map(Hermitian, Any[ eye(2), [0 1; 1 0], [0 -im; im 0], [1 0; 0 -1] ])
     @test ishermitian(σ)
 end
 
-# Hermitian matrix exponential/log
+# Hermitian matrix exponential/log/det
 let A1 = randn(4,4) + im*randn(4,4)
     A2 = A1 + A1'
     @test expm(A2) ≈ expm(Hermitian(A2))
     @test logm(A2) ≈ logm(Hermitian(A2))
     A3 = A1 * A1' # posdef
     @test expm(A3) ≈ expm(Hermitian(A3))
     @test logm(A3) ≈ logm(Hermitian(A3))
+    @test det(A2) ≈ det(Hermitian(A2))
+    @test det(A3) ≈ det(Hermitian(A3))
+    @test det(A4) ≈ det(Hermitian(A4))
 end
 
+# Symmetric matrix exponential/log/det
 let A1 = randn(4,4)
     A3 = A1 * A1'
     A4 = A1 + A1.'
+    @test det(A3) ≈ det(Hermitian(A3))
+    @test det(A3) ≈ det(Symmetric(A3))
+    @test det(A4) ≈ det(Hermitian(A4))
     @test expm(A4) ≈ expm(Symmetric(A4))
     @test logm(A3) ≈ logm(Symmetric(A3))
     @test logm(A3) ≈ logm(Hermitian(A3))