L2 norm and MSE

Relating $L_2$ norm to $\text{MSE}$

$$\begin{array}{rl}{L}_2& =||x_i-{\hat{x}}_i|{|}_2^2\\ & =\sum _i^N(x_i-{\hat{x}}_i{)}^2\\ & =\sqrt{N\cdot MSE(\vec{x},\vec{\hat{x}})}\\ & \iff \\ MSE(\vec{x},\vec{\hat{x}})& =L_2^2/N\end{array}$$