Difference between revisions of "Covector"

Latest revision as of 10:40, 12 June 2015

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^[1], that is given a vector space $(V,F)$, and its dual space, $V^*$ we say:

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

See also

• Covector applied to a tensor product

References

1. Jump up ↑ Liner Algebra via Exterior Products - Sergei Winitzki