For two vector, $\displaystyle b_{1} ,\ b_{2}$ and a matrix $\displaystyle A$:
$\displaystyle \begin{array}{{>{\displaystyle}l}} A\ \in \mathbb{R}^{n-1\times n} ,\ b_{1} ,\ b_{2} \ \in \ \mathbb{R}^{n\times 1} ,\ \end{array}$
I'm wondering what's the relationship between $\displaystyle < b_{1} ,\ b_{2}> \ $ and $\displaystyle < Ab_{1} ,Ab_{2}> $ ?