def METHOD_NAME(f_xx, f_xy, f_yx, f_yy, kappa=0, gamma1=0, gamma2=0, omega=0):
    """Left-multiplies the Hessian matrix of a lens with a distortion matrix with
    convergence kappa, shear gamma1, gamma2, and rotation omega:
    .. math::
        \\mathsf{H}'
        =
        \\begin{pmatrix}
        1 - \\kappa - \\gamma_1 & -\\gamma_2 + \\omega
        -\\gamma_2 - \\omega & 1 - \\kappa + \\gamma_1
        \\end{pmatrix}
        \\mathsf{H}
    :param f_xx: the i, i element of the Hessian matrix
    :param f_xy: the i, j element of the Hessian matrix
    :param f_yx: the j, i element of the Hessian matrix
    :param f_yy: the j, j element of the Hessian matrix
    :param kappa: the convergence
    :param gamma1: the first shear component
    :param gamma2: the second shear component
    :param omega: the rotation
    :return: the Hessian left-multiplied by the distortion matrix
    """
    f__xx = (1 - kappa - gamma1) * f_xx + (-gamma2 + omega) * f_yx
    f__xy = (1 - kappa - gamma1) * f_xy + (-gamma2 + omega) * f_yy
    f__yx = -(gamma2 + omega) * f_xx + (1 - kappa + gamma1) * f_yx
    f__yy = -(gamma2 + omega) * f_xy + (1 - kappa + gamma1) * f_yy
    return f__xx, f__xy, f__yx, f__yy