# Covector

From Maths

(Redirected from Linear functional)

**AKA:** Dual vectors, Linear forms, Linear functionals.

**More details can be found:** at Dual space

## Contents

## Definition

Covectors are the name of elements in the dual space of a vector space^{[1]}, 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

## References

- ↑ Liner Algebra via Exterior Products - Sergei Winitzki