While doing homework for a professor with notation completely different from my last semester professor's notation, I've become stuck trying to interpret what this means:
$$ v \rightarrow \langle-,v\rangle_V $$ where $\langle,\rangle_V$ is an inner product on a finite-dimensional real vector space, $V$. The entire question is to show that the above identifies $V$ with $V^*$.
Any help is appreciated!
This denotes a map $T:V\to V^*$, mapping $v\in V$ to $f_v\in V^*$, where $f_v:V\to \mathbb{R}$ is defined by $$f_v(x)=\langle x,v\rangle_V $$ for $x\in V$. The question is then to show that $T$ is an isomorphism.