It is written in my book that if

$\displaystyle T = T_{\nu_1 \cdots v_l}^{\mu_1 \cdots \mu_k} \hat{e}_{(\mu_1)}\otimes \cdots \otimes \hat{e}_{(\mu_k)}\otimes \hat{\theta}^{(\nu_1)}\otimes \cdots \otimes \hat{\theta}^{(\nu_l)}$ than

$\displaystyle T_{\nu_1 \cdots v_l}^{\mu_1 \cdots \mu_k} = T(\hat{\theta}^{(\mu_1)},\ldots, \hat{\theta}^{(\mu_k)},\hat{e}_{(\nu_1)},\ldots ,\hat{e}_{(\nu_l)})$

where $\displaystyle \hat{e}_{(\mu_{1 \cdots l})}$ are the basis of a vector space and $\displaystyle \hat{\theta}^{(\nu_{1 \cdots k})}$ are the basis of the correspondent dual vector space.

My question is why does the indexes $\displaystyle \mu$ and $\displaystyle \nu$ switch? In equation 1 $\displaystyle \mu$ is the index of $\displaystyle e$ but in 2 $\displaystyle \nu$ is the index of $\displaystyle e$. Should't $\displaystyle e$ and $\displaystyle \theta$ be switched in 1?