Covector

AKA: Dual vectors, Linear forms, Linear functionals.

More details can be found: at Dual space

Definition

Covectors are the name of elements in the dual space of a vector space, that is given a vector space [ilmath](V,F)[/ilmath], and its dual space, [ilmath]V^*[/ilmath] we say:

• [math]f^*\in V^*[/math] if [ilmath]f^*:V\rightarrow F[/ilmath] and [ilmath]f^*[/ilmath] is linear, recall linear means that:
  • [math]\forall x,y\in V\ \forall\alpha,\beta\in F[f^*(\alpha x+\beta y)=\alpha f^*(x)+\beta f^*(y)][/math]

See also

• Covector applied to a tensor product