$$\boldsymbol{a} \cdot \boldsymbol{b} = \left( \begin{array}{c} a_1 \\ a_2 \\ \vdots \\ a_n \end{array} \right) \cdot \left( \begin{array}{c} b_1 \\ b_2 \\ \vdots \\ b_n \end{array} \right) \\ = a_1b_1+a_2b_2+\cdots+a_nb_n \\ = |\boldsymbol{a}||\boldsymbol{b}|cos\theta$$ ただし$\theta$は$\boldsymbol{a}$と$\boldsymbol{b}$のなす角度.

$$\boldsymbol{x} \cdot \boldsymbol{x}\\ = x_1x_1 + x_2x_2 + \cdots + x_nx_n\\ = ||\boldsymbol{x}||^2$$