def linear_get_coefficients(coef, rhouv, s, i, j, k, u, v,
                            unfolding, matrix_form):
    r"""Get the indices mu, nu, and term coefficients for linear terms.

    We determine mu and nu, the indices labeling the density matrix components
          d rho[mu] /dt = sum_nu A[mu, nu]*rho[nu]
    for this complex and rho_u,v.

    >>> from fast.symbolic import define_density_matrix
    >>> Ne = 2
    >>> coef = 1+2j
    >>> rhouv = define_density_matrix(Ne)[1, 1]
    >>> s, i, j, k, u, v = (1, 1, 0, 1, 1, 1)
    >>> unfolding = Unfolding(Ne, real=True, normalized=True)

    >>> linear_get_coefficients(coef, rhouv, s, i, j, k, u, v,
    ...                              unfolding, False)
    [[1, 0, -2.00000000000000, False, False]]

    """
    Ne = unfolding.Ne
    Mu = unfolding.Mu
    # We determine mu, the index labeling the equation.
    mu = Mu(s, i, j)

    if unfolding.normalized and u == 0 and v == 0:
        # We find the nu and coefficients for a term of the form.
        # coef*rho_{00} = coef*(1-sum_{i=1}^{Ne-1} rho_{ii})
        if unfolding.real:
            ss = 1
        else:
            ss = 0

        mu11 = Mu(ss, 1, 1)
        muNeNe = Mu(ss, Ne-1, Ne-1)
        rhouv_isconjugated = False
        if s == 1:
            coef_list = [[mu, nu, im(coef), matrix_form, rhouv_isconjugated]
                         for nu in range(mu11, muNeNe+1)]
        elif s == -1:
            coef_list = [[mu, nu, -re(coef), matrix_form, rhouv_isconjugated]
                         for nu in range(mu11, muNeNe+1)]
        elif s == 0:
            coef_list = [[mu, nu, -coef, matrix_form, rhouv_isconjugated]
                         for nu in range(mu11, muNeNe+1)]
        return coef_list

    #####################################################################

    if (unfolding.lower_triangular and
       isinstance(rhouv, sympy.conjugate)):
        u, v = (v, u)
        rhouv_isconjugated = True
    else:
        rhouv_isconjugated = False
    # If the unfolding is real, there are two terms for this
    # component rhouv of equation mu.
    if unfolding.real:
        nur = Mu(1, u, v)
        nui = Mu(-1, u, v)
    else:
        nu = Mu(0, u, v)
    #####################################################################
    # We determine the coefficients for each term.
    if unfolding.real:
        # There are two sets of forumas for the coefficients depending
        # on whether rhouv_isconjugated.
        # re(I*x*conjugate(y)) = -im(x)*re(y) + re(x)*im(y)
        # re(I*x*y)            = -im(x)*re(y) - re(x)*im(y)
        # im(I*x*conjugate(y)) = +re(x)*re(y) + im(x)*im(y)
        # im(I*x*y)            = +re(x)*re(y) - im(x)*im(y)
        if s == 1:
            # The real part
            if rhouv_isconjugated:
                coef_rerhouv = -im(coef)
                coef_imrhouv = re(coef)
            else:
                coef_rerhouv = -im(coef)
                coef_imrhouv = -re(coef)
        elif s == -1:
            if rhouv_isconjugated:
                coef_rerhouv = re(coef)
                coef_imrhouv = im(coef)
            else:
                coef_rerhouv = re(coef)
                coef_imrhouv = -im(coef)

        coef_list = [[mu, nur, coef_rerhouv, matrix_form, rhouv_isconjugated]]
        if nui is not None:
            coef_list += [[mu, nui, coef_imrhouv,
                           matrix_form, rhouv_isconjugated]]
    else:
        coef_list = [[mu, nu, coef, matrix_form, rhouv_isconjugated]]

    return coef_list