Regarding nomenclature of a vector related to field automorphisms

Question

Is there a particular designation in use for the following type of vector, constructed by taking a collection of basis elements $\beta_1$, $\beta_2$, $\dotsc$, $\beta_n$ for a field extension, selecting an automorphism $\sigma$ of this extension, and evaluating it at the aforementioned basis elements term by term, namely, $(\sigma(\beta_1),\sigma(\beta_2),\dotsc,\sigma(\beta_n))$?