Eigenvalues of linearized RG

Consider RG transformation in the vicinity of a fixed point:
$$
K_n^prime=K_n^* + delta K_{n}^prime = K_n^* + sum_m frac{partial K^prime_n}{partial K_m} delta K_m + O(delta K^2)
$$
where
$M_{nm} = frac{partial K^prime_n}{partial K_m}$ is the matrix of linearized RG.

Using semigroup property of RG:
$$
R_{l_1} R_{l_2} = R_{l_2} R_{l_1} = R_{l_1 l_2}
$$
where $l$ is the scale we choose to integrate out.

we have
$$
M^{l_1} M^{l_2} = M^{l_2} M^{l_1} = M^{l_1 l_2}
Lambda^{(sigma)}_{l_1} Lambda^{(sigma)}_{l_2} = Lambda^{(sigma)}_{l_1 l_2}
$$
where $Lambda_l^{(sigma)}$ is the eigenvalues of $M^l$, $sigma$ used to label different eigenvalues.

Using above equation of eigenvalues, it can be shown that
$$
Lambda_l^{(sigma)} = l^{y_{sigma}}
$$

Here is my question, from above form it seems that $Lambda_l$ cannot be negative, but in
some problem, the eigenvalues are negative through concrete calculation. How can it be possible?