Add property method `is_hermitian` and `is_unitary`

src/base/properties.rs

@@ -119,4 +119,23 @@ where
         // TODO: improve this?
         self.clone_owned().try_inverse().is_some()
     }
+
+    /// Returns `true` if this matrix is hermitian.
+    #[inline]
+    #[must_use]
+    pub fn is_hermitian(&self) -> bool {
+        self.is_square() && self.transpose().conjugate().eq(self)
+    }
+
+    /// Returns `true` if this matrix is unitary.
+    #[inline]
+    #[must_use]
+    pub fn is_unitary(&self, eps: T::Epsilon) -> bool
+    where
+        T: Zero + One + RelativeEq,
+        T::Epsilon: Clone,
+    {
+        let r = self.transpose().conjugate() * self;
+        self.is_square() && r.is_identity(eps)
+    }
 }

tests/core/matrix.rs

@@ -201,6 +201,24 @@ fn identity() {
     assert!(!not_id3.is_identity(0.0));
 }
 
+#[test]
+fn is_hermitian() {
+    let a = Matrix2::new(1.0, 2.0, 3.0, 4.0);
+    let b = Matrix2::new(1.0, 2.0, 2.0, 1.0);
+
+    assert!(!a.is_hermitian());
+    assert!(b.is_hermitian());
+}
+
+#[test]
+fn is_unitary() {
+    let a = Matrix2::new(1.0, 2.0, 3.0, 4.0);
+    let b = Matrix2::new(0.0, 1.0, 1.0, 0.0);
+
+    assert!(!a.is_unitary(1.0e-7));
+    assert!(b.is_unitary(1.0e-7));
+}
+
 #[test]
 fn coordinates() {
     let a = Matrix3x4::new(11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34);