code: def diagonalize_real_symmetric_matrix(
          matrix: np.ndarray,
          *,
          rtol: float = 1e-5,
          atol: float = 1e-8) -> np.ndarray:
      
  
      # TODO: Determine if thresholds should be passed into is_hermitian
      if np.any(np.imag(matrix) != 0) or not predicates.is_hermitian(matrix):
          raise ValueError('Input must be real and symmetric.')
  
      _, result = np.linalg.eigh(matrix)
  
      return result
docs: Returns an orthogonal matrix that diagonalizes the given matrix.
  
      Args:
          matrix: A real symmetric matrix to diagonalize.
          rtol: float = 1e-5,
          atol: float = 1e-8
  
      Returns:
          An orthogonal matrix P such that P.T @ matrix @ P is diagonal.
  
      Raises:
          ValueError: Matrix isn't real symmetric.