Relation between simple roots and fundamental weights.

Question

Let $\alpha_1, \ldots, \alpha_n$ be simple roots of a semisimple complex Lie algebra. Let $\omega_1, \ldots, \omega_n$ be the fundamental weights. We have $$ \alpha_i = \sum_{s} k_s \omega_s, $$ for some $k_s \in \mathbb{C}$. Therefore $$ (\alpha_i, \alpha_j^{\vee}) = \sum_{s} k_s (\omega_s, \alpha_j^{\vee}) = k_j. $$ On the other hand, $(\alpha_i, \alpha_j^{\vee})=C_{ij}$, where $C_{ij}$ is the $(i,j)$ entry of the Cartan matrix $C$. Therefore $k_j = C_{ij}$ and hence $$ \alpha_i = \sum_{j} C_{ij} \omega_j. $$ But some books define that $(\alpha_i, \alpha_j^{\vee})=C_{ij}$ and some other books define that $(\alpha_i, \alpha_j^{\vee})=C_{ji}$. Do we have $\alpha_i = \sum_{j} C_{ij} \omega_j$ or $\alpha_i = \sum_{j} C_{ji} \omega_j$? Thank you very much.