Implement singular_values

Author: user202729

src/sage/matrix/matrix2.pyx

@@ -6992,6 +6992,37 @@ cdef class Matrix(Matrix1):
                         extend=extend, algorithm=algorithm,
                         suppress_future_warning=False))
 
+    def singular_values(self) -> Sequence:
+        """
+        Return a sequence of singular values of a matrix.
+
+        EXAMPLES::
+
+            sage: A = matrix([[1, 2], [3, 4]])
+            sage: A.singular_values()
+            [0.3659661906262578?, 5.464985704219043?]
+
+        TESTS::
+
+            sage: type(A.singular_values())
+            <class 'sage.structure.sequence.Sequence_generic'>
+            sage: set_random_seed(100)
+            sage: A = matrix.random(CC, 5)
+            sage: Sequence((A*A.H).eigenvalues(), universe=RR)
+            Traceback (most recent call last):
+            ...
+            TypeError: unable to convert ... to an element of Real Field with 53 bits of precision
+            sage: A.singular_values()  # abs tol 1e-13
+            [0.317896596475411, 1.25232496300299, 1.48403213017074, 2.08062167993720, 2.59091978815526]
+        """
+        from sage.rings.abc import ComplexField
+        e: Sequence = (self*self.H).eigenvalues()  # guaranteed to be real
+        R = self.base_ring()
+        if isinstance(R, ComplexField):
+            # because of floating point error e may not be all real
+            e = Sequence([x.real() for x in e], universe=R._real_field())
+        return Sequence([x.sqrt() for x in e])
+
     def _eigenvectors_result_to_eigenvalues(self, eigenvectors: list) -> Sequence:
         """
         Convert the result of :meth:`eigenvectors_left` to a sequence of eigenvalues