Dual Space

Statements

Definition. (L. W. Tu - An Introduction to Manifolds) Let $V$ and $W$ be real vector spaces, the vector space composed of all linear maps $f:V\to W$ is denoted by Hom$(V,W)$. The dual space $V^V$ of $V$ the is the space of all real-valued linear functions on $V$ $V^V=\text{Hom}(V,\mathbb{R}).$ The elements of $V^V$ said to be covectors or $1-$covectors on $V$.