Dual vectors are the members of a dual space.

In the context of tensors , we use raised indices to refer to members of the dual basis vs the underlying basis:
The dual basis vectors $e_{i}$ are defined to "pick the corresponding coordinate" out of elements of V. E.g.:
By expanding into the basis, we can put this more succinctly with the Kronecker delta as:

$e_{1}e_{2}e_{3}e_{1}e_{2}e_{3} ∈V∈V∈V∈V_{∗}∈V_{∗}∈V_{∗} $

$e_{1}(4,−3,6)e_{2}(4,−3,6)e_{3}(4,−3,6) =4=−3=6 $

$e_{i}(e_{j})=δ_{ij}$

Note that in Einstein notation, the components of a dual vector have lower indices. This works well with the upper case indices of the dual vectors, allowing us to write a dual vector $f$ as:

$f=f_{i}e_{i}$

In the context of quantum mechanics, the bra notation is also used for dual vectors.