Let \(A\) be a mixed tensor field of type \((k,l)\). Then for given coordinates it can be written as
\begin{equation*} A^{i_1,\ldots,i_k}_{j_1,\ldots,j_l}\frac{\partial }{\partial x^{i_1}}\otimes \cdots \otimes \frac{\partial }{\partial x^{i_k}}\otimes dx^{j_1}\otimes \cdots \otimes dx^{j_l}. \end{equation*}The real valued functions \(A^{i_1,\ldots,i_k}_{j_1,\ldots,j_l}\) are called components of \(A\).
Remark
- In the case \(A\) is a covariant vector field, we obtain its componets similiar to the ones of the covector field, i.e. \begin{equation*} A_{i_1,\ldots,i_k}=A\biggl(\frac{\partial }{\partial x^{i_1}}, \ldots, \frac{\partial }{\partial x^{i_k}}\biggr). \end{equation*}