Dual vector space

Here a vector space is denoted as [math](V,K)[/math] where [math]K[/math] is the field the vector space is over.

Definition

Suppose [ilmath]V[/ilmath] and [ilmath]W[/ilmath] are two real vector spaces, we denote by [math]\text{Hom}(V,W)[/math] ("Hom" is short for homomorphism) the vector space of all linear maps [math]f:V\rightarrow W[/math]

The Dual space [math]V^*[/math] or [math]V^\vee[/math] is [math]\text{Hom}(V,\mathbb{R})[/math], that is the vector space of all real-valued linear functions on [math]V[/math]

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