Olympiad Algebra and Analysis

Let $n\geq2$ be an integer and specify signs $\epsilon_1 = +1$ and $\epsilon_2 = \dots = \epsilon_n = +1$. For $\vec{x}, \vec{y} \in \mathbb{R}^n$, define the bilinear form $$Q( \vec{x}, \vec{y}) = \sum_{i=1}^{n} \epsilon_i x_i y_i.$$