[[Linear algebra MOC]]
# Dual vector space

Let $V$ be a [[vector space]] over a [[field]] $\mathbb{K}$.
The **dual vector space** $V^*$ is the space of all linear functionals $V \to \mathbb{K}$,
i.e. $V^* = \Vect_{\mathbb{K}}(V,\mathbb{K})$. #m/def/linalg 
Elements of this space are called **dual vectors** or **covectors** of $V$.

- In the context of [[Topological vector space|TVSs]] we consider $\cat{TopVect}_{\mathbb{K}}(V,\mathbb{K})$

A covector is an example of [[Tensor]], and are important in the general definition of these objects.

#
---
#state/develop | #lang/en | #SemBr