I would appreciate your help on the following problem:

Given the vectors $\displaystyle \vec{u}=(2,-3,4,5)$ and $\displaystyle \vec{v}=(3,4,-7,8)$

1) Viewing the Inner Product Rule as a type of two vector transform, what can you say about $\displaystyle \vec{v}$?

2) Would this pseudo inner product rule correspond to a one-to-one transform?