Dual vector space

Here a vector space is denoted as $$(V,K)$$ where $$K$$ is the field the vector space is over.

Definition

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

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

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