- Thread starter
- #1

- Feb 5, 2012

- 1,621

Here's a question that I have now clue on how to solve. I hope you can shed some light on it.

**Question:**

Let $f:V\times V\rightarrow F$ be a nonsingular bilinear function on a vector space $V$ over a field $F$. Prove that for any linear function $\psi\in V^*$ there is unique $v\in V$ such that $\psi(x)=f(x,\,v)$, for any $x\in V$, and that the map $v\rightarrow \psi$ is an isomorphism of $V$ and $V^*$.